Case study comparing from Q-system and Terzaghi’s Rock Load

Classification

*Han Fook Kwang and Cho Man-Sup1)

1)
SK E&C, Singapore

ABSTRACT

This paper compares Terzaghi’s Rock Load Classification System against the
empirical method adopted for the Q-system based on the case study of a constructed
mined tunnel. The rock load estimated from the Terzaghi’s Rock Load Classification
method was obtained by correlating site tunnel convergence monitoring of a mined
tunnel with a back analysis of a 3-D numerical model of the mined tunnel. The rock
load estimated from the Q-system empirical method was based on the Q-value and the
static modulus of deformation observed from the field.

Key words: Face mapping, support pressure, mined tunnel numerical model,
instrumentation.

1. INTRODUCTION
Over the years the Q-system had been used widely for the design of mined
tunnels. The Q-system had been constantly revised to suit the various usage in
particular for the design of the supporting requirements of mined tunnels through case
studies from previous tunnels. Often the Q-system had also been compared against the
other rock mass classification methods to identify the most appropriate supporting
system. This paper attempts to compare the support pressures estimated from the Q-
system and the Terzaghi’s Rock Load Classification method in the lining system based
on the site monitoring results obtained from a mined tunnel constructed in Singapore.

In 2012 SP Power Assets Ltd commissioned the construction of two networks of

deep cable tunnels; in the directions of North-South and East-West alignments. The
entire length of the tunnels are 35km across Singapore.

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 Figure 1.1 Alignments of cable tunnel

The North-South alignment is approximately 18.5km long from Gambas shaft (in
the north) to May shaft (in the south) with a total of 7 shafts. This paper discusses the
Tagore Shaft design located along the North-South Contract alignment.

1.1 Tagore Shaft

The shaft consists of a 14m clear inner diameter vertical shaft constructed via
controlled blasting and temporarily supported by shotcrete lining. The overall depth of
the vertical shaft is approximately 65m deep. The mined tunnel layout at the bottom of
the shaft consists of a 9.5m high by 11m wide adit tunnel linking to 2 nos 8.5m high by
8.5m wide enlargement tunnels via a junction [8].

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 Figure 1.2 Overall isometric layout Figure 1.3 Shaft and tunnel cross section

Based on the Contract Specifications, the mined tunnel was to be completed with
an insitu permanent lining enveloped within the temporary shotcrete lining. Therefore
the finished tunnel system to be adopted was a Double Shell Lining (DSL) tunnel.
Waterproofing was provided via a membrane laid between the linings [8].

2. OBJECTIVE

This paper aims to compare the rock loads estimated from the Terzaghi’s Rock
Load Classification method via correlating the back analysis of a set of temporary lining
models with the tunnel convergence monitoring obtained from the field instrumentation
against the Q-system empirical method.

3. TAGORE SITE CONDITION

With reference to the Geological Map of Singapore (DSTA, 2009), the Tagore
Shaft is located in Bukit Timah Granite zone as shown in the map. In Singapore, Bukit
Timah forms one of the major formations and it is recognized as the base rock as it
underlies all other formations.

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 Figure 3.1 Geological map of Tagore Shaft

Bukit Timah Granite predominately includes granite and other less common rocks
such as adamellite, granodiorite, and diorite. In terms of mineralogy contents, Bukit
Timah Granite composes with quartz (30%), fieldspar (60-65%), biotite and hornblende
(less than 10%). In general, the texture of Bukit Timah Granite is medium to course
grained, light grey colour (sometimes pinkish – orthoclase), however, greenish dark
grey, course grained Granite was encountered at during Tagore Shaft excavation.

The rock head levels are largely undulating at Tagore Shaft location, ranging
from 20m (shaft side) to 42m (adit and enlargement sides) and overlain by residual soil
with small extent of peaty clay and sand layers. The mined tunnels were constructed
approximately 35m below the rock head level at approximately 60m below ground level.
The inclusions and intrusions within the Bukit Timah Granite in the form of dykes and
fault zones were encountered during the mined tunnel work.

At approximately 56m to 58m depth, a dark greenish grey, medium grained

DIORITE Dyke was encountered during adit excavation and rock mapping as a dyke
and highly fractured zone were encountered. Although a dyke and fault zone were
encountered during adit tunnel excavation, generally the crown and face were found to
be fairly stable and insignificant water ingress observed. The figure below shows the
exposed rock face of the heading excavation (during the face mapping phase) which
illustrates the varying quality of rock encountered during the mining activities.

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 Figure 3.2 Face mapping for tunnel heading

No insitu testing was carried out for the Uniaxial Compressive Strength for Rock
Mass. Instead the values for GIII and GII were estimated as 0.5 MPa and 3.5 MPa
respectively for mined tunnel (Drill and Blast), setting s’3 = 0, based on the GSI and
intact UCS values using the Hoek-Brown equation (Hoek, Carranza-Torres and Corkum,
2002) as follows [7];

sc = sci . sa Eq. (1)

Where: s = exp [(GSI – 100) / (9 – 3D)] Eq. (2)

a = 1/2 + 1/6 x (e-GSI / 15 – e-20/3) Eq. (3)

4. INSTALLED TEMPORARY LINING SUPPORT

According to the face mapping Q-value results, various combinations of shotcrete

thicknesses and rockbolts were installed in accordance to the design. Below figure
shows the face mapping results carried out for the heading.

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 Figure 4.1 Face mapping results

Following the face mapping results, the general thickness of shotcrete applied
was 250-200mm thick with 4.5m long, 25mm thick rockbolts installed at approximately
1.5m (radially) by 1.2m (longitudinally) spacings.

5. DESIGN ANALYSIS METHODOLOGY

The geometry and layouts of the numerical model was derived from Building
Information Modeling (BIM). The Permanent Lining design was carried out in
accordance to the Singapore Power Assets Ground Interpretation Baseline Report
(GIBR) [7] and Contract Specifications Design Criteria for the design of the permanent
linings.

Prior to the tunnel mining works, Type 1 Temporary Lining numerical model was
created (based on the similar geometry and layouts as the permanent model) for the
estimation of the convergence monitoring limit, which was adopted as 10mm, for the
mined tunneling works.

During the actual tunnel mining works, a set of Type 2 Temporary Lining
numerical models (based on the similar geometry and layouts as the permanent model)
were created with a range of rock loads and springs. Displacements from these models
were compared with onsite convergence monitoring at similar locations to identify the
most probable rock load in accordance with the Terzaghi’s Rock Load Classification
method.

Based on the Q-value observed onsite, the Q-system rock load was calculated
in accordance with the Q-system empirical method.

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6. NUMERICAL ANALYSIS

Ground Investigations were carried out on site via boreholes and laboratory tests
for the design input assumptions for the numerical modeling. Key assumptions for both
Permanent and Temporary Lining models adopted were in accordance to the GIBR and
utilized the Terzaghi’s Rock Load Classification method. Rock assumed for the design
was GIII, the density of the rock adopted was 24kN/m3 [7].

Figure 6.1 Numerical model of shaft and tunnel

Figure 6.2 Terzaghi rock load factor diagram

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 Table 6.1 Terzaghi’s Rock Load Classification

6.1 Permanent Lining Numerical Model

Flat mesh plates were created to be approximately 1m by 1m with fixed joints and
0.3 MPa compression-only springs activiated in the Z-axis (perpendicular to the plates).
Boundary conditions of the 3-D Permanent Lining model was checked with a 2-D Plaxis
model. Both models were checked for similar tunnel and shaft deformation magnitudes.

The plates were modelled to be reinforced concrete walls and slabs with
thicknesses to the design as shown below.

Element Thickness
Adit Tunnel 0.5m
Adit Tunnel Base Slab 1.2m
Enlargement Tunnel 0.5m
Enalgement Tunnel Base Slab 1.0m
Junction Crown 0.5m
Junction End Wall 1.5m
Junction Base Slab 2.0m

Table 6.1 Permanent Lining member thickness

In addtion to the provision of waterproofing membrane, crack widths checks of the

reinforced concrete was limited to 0.25mm for external face and 0.3mm to internal face
[8]. Hydrostatic pressures were modelled to full height at ground level. Lateral loading
to the tunnels and shaft was considered. Load safety factors adopted for all loads were
1.4 ULS and 1.0 SLS.

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 Horizontal stresses applied to the model were 0.8 and 1.2 times the overburden
stress. The Ko values were recommended by SPPA GIBR [7].

Rock classification was estimated with boreholes carried out prior to the works
and the upper levels of the shaft rock excavations. The rock was estimated to be very
blocky and seamy. The overburden rock load adopted was the more onerous between
Terzaghi Rock Load Classification method [8] and Unal Formula using RMR System
which were calculated to be 0.25 MPa and 0.092 MPa respectively. The overburden
rock load was applied to the top 120 degress of the tunnel crown The completed
approved design was later reviewed during the tunnel face mapping results.

Figure 6.1 Section of shaft for mapping Table 6.2 Shaft mapping results

Figure 6.2 Tunnel layout for mapping Table 6.3 Tunnel mapping results

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6.2 Type 1 Temporary Lining Numerical Model

The Temporary Lining model was similar to the Permanent Lining model in terms
of geomerty and layouts and with flat mesh plates were created to be approximately 1m
by 1m.

Spring supports were spaced uniformly around the circumfrence of the tunnels
and shafts at similar spacings and tension capacity of the actual rockbolts used in the
mined tunnel.

Where no rockbolts are located, rock springs with 0.3 MPa compression-only
springs were included to simulate the resistance from the rock mass. These rock and
rock bolt springs were only activated in the direction perpendicular to the meshed
plates (i.e Z-axis), the other axes were released. The moments for these springs were
also released.

The meshed plates were modelled to be 500mm thick concrete elements to

simulate the average applied shotcrete thickness. The applied shotcrete was Fibre
Reinforced Concrete however to be convservative, the model adopted plain concrete
elements. No base slab, lateral loading and hydrostatic pressure were modelled.

The overburden loading applied was similar to the Permanent Lining model i.e
0.25 MPa applied to the crown at approximately 120 degress.

6.3 Type 2 Temporary Lining Numerical Model

The model parameters, layout and geometrical inputs were similar to the Type 1
Temporary Lining model where no base slab, lateral loading and hydrostatic pressures
were not modelled.

The overburden rock load adopted were based on Terzaghi’s Rock Load
Classification method using the similar very blocky and seamy (classification as the
Permanent Lining model) providing a range 0.35 to 1.10(B+Ht) for the overburden load.

Based on the range of factors (i.e 0.35 to 1.10), different vertical overburden loads
were computed with an assumed rock density of 24 kN/m3 and varying rock springs
applied (i.e 0.1 MPa, 0.2 MPa, 0.3 MPa, 0.4 MPa and 0.5 MPa) to the numerical model.
The nodal displacements of the model were comparied at similar locations to the
measured onsite convergence monitoring results.

Rock loads were applied as vertical overburden on the top 120 degress of the
tunnel crown. No lateral loads was applied to the tunnel walls on the sides in the
numerical model because this was considered to be more conservative. Ko = 0.8 was
adopted as recommended in the SPPA GIBR [7] for the lateral loads which were
applied only to the shaft walls.

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 Combination Load case considered
Rock Load factor 0.35 1. Selfweight
2. Adit vertical overburden (172.2 kN/m2)
3. Enlargement overburden (142.8 kN/m2)
4. Shaft lateral load (137.76 kN/m2)
Rock Load factor 1. Selfweight
0.4 2. Adit vertical overburden (196.8kN/m2)
3. Enlargement overburden (163.2 kN/m2)
4. Shaft lateral load (157.44 kN/m2)
Rock Load factor 1. Selfweight
0.5 2. Adit vertical overburden (246 kN/m2)
3. Enlargement overburden (204 kN/m2)
4. Shaft lateral load (196.8 kN/m2)
Rock Load factor 1. Selfweight
0.6 2. Adit vertical overburden (295.2 kN/m2)
3. Enlargement overburden (244.8 kN/m2)
4. Shaft lateral load (236.16 kN/m2)
Rock Load factor 1. Selfweight
0.7 2. Adit vertical overburden (344.4 kN/m2)
3. Enlargement overburden (285.6 kN/m2)
4. Shaft lateral load (275.52 kN/m2)
Rock Load factor 1. Selfweight
0.8 2. Adit vertical overburden (393.6 kN/m2)
3. Enlargement overburden (326.4 kN/m2)
4. Shaft lateral load (314.88 kN/m2)
Rock Load factor 1. Selfweight
0.9 2. Adit vertical overburden (442.8 kN/m2)
3. Enlargement overburden (367.2 kN/m2)
4. Shaft lateral load (354.24 kN/m2)
Rock Load factor 1. Selfweight
1.0 2. Adit vertical overburden (492 kN/m2)
3. Enlargement overburden (408 kN/m2)
4. Shaft lateral load (393.6 kN/m2)
Rock Load factor 1. Selfweight
1.1 2. Adit vertical overburden (541.2 kN/m2)
3. Enlargement overburden (448.8 kN/m2)
4. Shaft lateral load (432.96 kN/m2)

Table 6.4 Numerical Model Load Combinations

7. ONSITE CONVERGENCE MONITORING FOR ESTIMATING ROCK LOADS

Convergence monitoring of the mined tunnel was carried out via a series of 3-D
prisms located at specific intervals throughout the tunnels which were installed during
the mining phase.

The convergence array adopted for this paper as shown below was located
approximately 20m from the shaft-adit tunnel. The excavation for this location was
carried out on the 5 Jan 2015, the array was installed on the 17 Jan 2015
approximately 8m from the tunnel face after 4 rounds of blasting and advancements.

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 Figure 7.1 Onsite convergence monitoring points

Both Terzaghi’s Rock Load and the Q-system empirical methods assume the
tunnel sections to be constant where the rock loads were applied in a 2-dimensional
space. The mid-point of the adit tunnel convergence monitoring was adopted because
it was considered that there was sufficient length of tunnel distance away from shaft
and junction areas that could affect the convergence results due to the 3-dimensional
geometrical effects during the mining works.

The following graphs show the studies carried out for each convergence
monitoring point comparing the 5 different rock springs (i.e 0.1 MPa, 0.2 MPa, 0.3 MPa,
0.4 MPa and 0.5 MPa) with the range of overburden loadings (i.e 0.35-1.1(B+H))
against the site monitored measurements.

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 From the above graphs, the most probable rock spring to be 0.2 MPa and the
most probable applied rock load factor to be 0.4(B+H) = 196.8kN/m2.

Figure 7.2 Collated information from convergence, rock spring and rock load

8. Q-SYSTEM EMPIRICAL METHOD

The Q-value observed at the adit location adopted for the numerical model
approximately 20m from the shaft-adit junction location was 22.5 (see Table 6.3 Tunnel
Mapping results). The depth of the tunnel at this location from the ground level to the
tunnel crown is approximately 58.5m while the tunnel height and width is 9.5m and 11m
respectively.

The empirical equation for estimating the rock load (support pressure) [5] is

Pr = 0.1Q-1/3 (MPa) Eq. (4)

Previous papers have found the correlation between the support pressures to be
inversely proportional to the static modulus of deformation Em [4, 5]. Therefore the
equation [9] is

Pr = 1/Em (MPa) Eq. (5)

Where, Em = 25logQ (GPa) for Q > 1

From the above equations (4) and (5), the rock load was calculated to be
35kN/m2 for equation (4) and 29.6kN/m2 for equation (5). The range can be considered
small, therefore the anticipated rock loads from both equations can be considered
acceptable.

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 Support pressures was found to be inversely proportional to deformation modulus,
a central trend for tunnel deformation is that Δ in millimeters is equal to the span in
meters divided by Q [4]. Therefore, the equation gives

Δ = Span / Q (mm) Eq. (6)

Convergence 5 was selected for the Terzaghi Rock Load method, the span to be
adopted shall be the similar length as convergence 5 which was estimated to be 11.7m.
Hence equation (6) gives a Δ of 0.52mm. The recorded convergence was recorded to
be 5.2mm which should be considered to be the total movement throughout the mining
procedure that includes the vibrations from the blasting phase, therefore such small
movements can be reasonable.

9. CONCLUSIONS

The numerical model created was a wish-in place model without considerations
for the staged construction sequence and the stabilization of the rock through the
cumulative loosening process during the mining process. During the excavation
sequences of the mined tunnel, the intact rock mass would have been disturbed and
some beneficial rock loosening may have taken place. By the time of the excavation of
the rock at that location, the rock mass would have stabilized thereby recording small
displacements at the excavated face.

Therefore the displacements obtained from the numerical model should be

considered as the total displacement which can be expected to be larger than the
actual displacement due to the rock load of the excavated tunnel.

This explains the phenomenon where the monitored convergences obtained are
generally smaller than the convergences obtained from the numerical model. However
one must remember that the monitored convergences includes the vibrations effects
from the blasting during the mining phase. This implies that the actual applied rock load
should be lesser.

Ground investigations carried out prior to the excavations suggested the rock
quality to be Blocky to Seamy and Good to Fair. Throughout the mining process, the
rock mass at the tunnel level was found to be Blocky and Good. This suggested that
the rock mass strength should be 3.5 MPa or higher which would be more than the
values adopted by all the numerical models. Therefore the displacements obtained
from the numerical models will had been conservative.

The Terzaghi’s Rock Load Classification method for rock loads provides
reasonable support pressure estimates for small tunnels but over estimates for tunnels
having diameter more than 6m [2] and is generally applied to softer and/or weaker
rocks condition with lower rock mass shear strength. Therefore the 196.8kN/m2 [i.e
0.4(B+H)] rock load and 0.2 MPa rock spring discussed in this paper can still be
considered to be conservative.

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 As mentioned above the quality of rock from site observations was found to be
good, the Q-system empirical method discussed in this paper found to be
approximately 5 times smaller at 35kN/m2 can be considered to be reasonable since Q-
system is best utilized for drill and blast tunnels [8].

This is consistent with author’s opinion where the rock load obtained from Q-
system empirical method should be lesser than the numerical method which would be
more realistic to the actual case. Measured site convergence was also recorded to be
small, i.e the largest measured was approximately 5.2mm (in total displacement). This
is further evident in the small change in movement estimated to be 0.52mm.

The above observations and findings further supports the author’s opinion that the
rock loads obtained from Q-system is considered more reasonable for good quality rock
with sufficient rock cover.

Understanding and adopting the suitable method based on the competency of the
rock condition can help future tunnels to have an economical design whilst maintaining
a safe environment during the construction process. This will also allow designers to
better estimate the rock load to apply for more realistic and economical design for
future deep tunnels.

10. ACKNOWLEDGMENTS

The author would like to acknowledge the Singapore Power Assets Ltd and SK
Engineering & Construction (Singapore) for their co-operation, review of the paper and
agreement to utilize their data collected.

The author would also like to thank colleagues Defence Science Technology
Agency Singapore, in particular Dr Zhou Yingxin, and at WSP / Parsons Brinkerhoff for
their time and efforts in their review of this paper.

REFERENCES

1. Arild Palmstrom & Einar Broach (2006), “Use and misuse of rock mass
classification systems with particular reference to the Q-system”

2. B.Singh & R.K Geol (1999), “Rock mass classification: a practical approach in
civil engineering: Amsterdam”, Elsevier Science

3. E.Grimstad & N.Barton (1993), “Updating the Q-system for NMT”

4. N.R Barton (2013), “Integrated empirical methods for the design of tunnels,
shafts and caverns in rock, based on the Q-system”

5. N.Barton (2002), “Some new Q-value correlations to assist in site

characterization and tunnel design”

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6. NGI 2015, “Using the Q-system, Rock mass classification and support design”

7. Singapore Power Asset (North-South Contract 2) Geological Baseline report

8. Singapore Power Asset (North-South Contract 2) Design Criteria and

Performance Specifications, Civil and Structural Works

9. Syed Muntazir Abbas & Habil Heinz Konietzky (2016), “Rock Mass Classification
Systems”

10. Terzaghi, K. (1946, pp15-99), “Rock Defects and Loads on Tunnel Supports, In
Rock tunneling with Steel Support” eds R.V Proctor and T.L. White, Commercial
Shearing Co., Youngstown, OHIO

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