► PROBLEMS

PROBLEM 1
A 200-cm borehole log ofa rock is illustrated below. Find the RQD for this
rock sample.
Core length = 200 cm

24cm 40cm 23 cm 41cm 44cm 9 cm 13 cm

~~ :...1?~~~tf1,!~lt!ii,l
Rock pieces < 10 cm Mechanical break
No Recoııery

caused by drilling

A) RQD = 36.6%
B) RQD = 51.8%
C) RQD = 7 4.5%
D) RQD = 90.8%
PROBLEM 3
A tunnel is to be driven through a weathered quartz with the following
characteristics:

➔ A point-load strength index of 4 MPa.

➔ A RQD of 65%.
➔ Spacing between joints is 450 mm.
➔ Joints are slightly rough and have a separation less than 1 mm. Walls are highly
weathered .
➔ Tunneling conditions are anticipated to be damp.
➔ The dominant joint set dips at 30° against the direction of the drive.

What is the RMR of this rock mass?

A) RMR =29
B) RMR=48
C) RMR = 63
D)RMR=80

PROBLEM 11
Adam foundation is to be built upon a strong limestone with the following
cha racteristics:

➔ Uniaxial compressive strength of 80 MPa.

➔ A RQD of 80%.
➔ Spacing between joints is 80 mm.
➔ The joint set has been described as follows:
➔ Average discontinuity length is 4 m.
➔ Separation of joints is generally less than 0.1 mm.
➔ Joints
are slightly rough and moderately weathered.
➔ Joints have no infilling.
➔ Groundwater conditions are assumed to be dripping.
➔ The discontinu ity orientation was deemed fair.

What is the RMR of this rock mass?

A\nıAn _,,.
➔ The RQD is 80%.
➔ The rock mass contains one joint set controlling stability.
➔ Joints are rough, irregular and undulating.
➔ There are unaltered joint walls with some surface staining.
➔ There is medium hydraulic inflow with occasional outwash of joint fillings.
➔ Stress conditions were deemed favorable to the excavation.

What is the rating of this rock mass in the Q-system? Use the average stress
reduction f actor (SRF) if Table 6 happens to suggest a range of values. Further, use
the new SRF values if the stress fıeld category is associated w ith old and new
values. The latter values were taken from the 1993 review of the system.
A) Q = 0.86

B)Q=15.1
C) Q = 79.2
D)Q = 141

PROBLEM 6
A small cavern will be excavated a mass of limestone w iith UCS of 39 MPa.
The characteristics of the rock mass are as follows:

➔ The RQD is 60%.

➔ The rock mass contains one joint set controlling stability plus a subset of
random joints.
➔ Joints are smooth and planar.
➔ Rock wall contact before 1O cm shear. Strong overconsolida tion. There are thin,
continuous fıllings of non-softening clay mineral.
➔ The excavation intersects multiple weakness zones containing non-swelling clay
minerals and dlsintegrated rock.
➔ There is large hydraulic inflow with substantial outwash of joint fıll ings.

What is the rating of th is rock mass in the Q-system? Use the average stress
reduction factor (SRF) if Table 6 happens to suggest a range of values. Further, use
the new SRF values if the stress fıeld category is associated with old and new
values. The latter values were taken from the 1993 review of the system.
A) Q = 0.11
B) Q = 5.8
C) Q = 67.5
D) Q = 120
 ► SOLUTIONS

P.l ■ Solution
The RQD is given by

RQD = tLength of core pieces > l O cm

Total length of core run

Accordingly,

RQD = 24+40+41+44 =1?4 .S¾\

200
This RQD indicates a rock with fair to good quality.
1
ı
The correct answer is C.
P.3 ■ Solution
Fer a point-load strength index of 4 MPa, Table 1-A1 gives a rating of 12.
Fer a RQD between 50 and 75%, Table 1-A2 gives a rating of 13. Fer a discontinuity
spacing of 450 mm, Table 1-/:B gives a rating of 1O. Fer slightly rough joints with
the specified separation and highly weathered walls, Table 1-A4 gives a rating of
20. Fer the specified groundwater conditions, Table 1-A5 gives a rating of 1O.
Lastly, Table 1-F gives a description of 'favorable' if the tunnel is to be driven
against the dip ofa set of joints dipping at 30°. Referring to Table 1-B with this
classification, we read a rating adjustment of -2. Gathering this information, the
RMR is found as

RMR = 12+ 13+ 10+20+ 10-2 = ~

According to Table 1-C, the mass in question fits into the 'good rock'
category.

The correct answer is C.

 glves a
is 2 + 5 + 3 + 6 + 3 = 19. For drippln g ground water condltio ns, Table 1-AS
rating of -
ratlng of +4. For 'fa lr' dlscont inulty condltions, Table 1-8 gives c1 penalty
7. Gleanln g this lnformat ion, the RMR is found as

RMR =12 + 17 + 8 + 19 + 4 - 7 =ITI]

y.
As per Table 1-C, the mass consldered belongs to the 'fair rock' categor

The correct answer is B.

P.5 ■ Solu tion

r /ıı
For one set of joints govern lng stability, Table 2 gives a joint set numbe
ess
= 2.0. For rough, irregula r and undula ting joints, Table 3 gives a joint roughn
4 gives a
numbe r lr = 3.0. For unalter ed joint walls with surface staining only, Table
h of
joint alterati on numbe r / 0 = 1.0. For medium inflow wlth occasional outwas
joint fıllings, Table 5 gives a joint water reduction numbe r lw = 0.66. The
principal
overbu rden stress will not surpass 1O MPa, which is to say that the major
stress will be a1 = K x 1O= 4/3 x 1O= 13.3 MPa at most. This gives a ratio
a, / a1 =
ratio
160/ 13.3 = 12.0. Referring to Table 6 with this quantit y, we see that, tora
a, / a1 ranging from 10.0 to 200 and favorable stress conditions, the SRF should be
mass,
taken as 1.0. We are now in position to evaluate the Q-value for this rock

to
According to Table 7, the mass in questio n is just above the threshold
be classifıed as 'very good' rock.

The correct answer is C.

P.6 ■ Solut ion

For one set of joints govern ing stability plus random, Table 2 gives a joint
rough ness
set numbe r / 11 = 3.0. For smooth and planar joints, Table 3 gives a joint
numbe r f r = 1.0. For rock wall contact before 1O cm shear, strongl y
on
overconsolidated, non-so ftening clay minera l, Table 4 gives a joint alterati
Table
number l a = 6.0. For large inflow with considerable outwas h of joint fillings,
ts multipl e
5 gives a joint water reduction fw = 0.33. Since the excavation intersec
s a SRF of
weakness zones contain ing clay and disinteg rated rock, Table 6 indicate
1O.O. We can then establish the Q-value for this rock mass,

to
According to Table 7, the mass in questio n is just above the thresho ld
be classified as 'very poor' rock.

The correct answer is A.