UNIVERSITY OF MORATUWA, SRI LANKA

Department of Civil Engineering

M.Sc. / P.G. Diploma in Geotechnical Engineering

Semester 1 Examination (2022)

CE 5414 Rock Mechanics

Time allowed : 3 hours + 15 minutes for reading August 2022

This paper contains 4 questions and 6 pages, including this page.

Answer All Questions

This examination accounts for 75% of the module assessment.

The maximum marks attainable are approximately indicated in square brackets.

This is an open book examination and is conducted in the on-line mode.

The time allocated for answering the examination is 3 hours.

This online examination will be conducted via Moodle platform. Zoom link for the exam will
be posted in Moodle.

At the end of examination duration, there will be a 20-minute time allocation for uploading
the scanned pages of the answer script in pdf format. Scanning should be done within the first
05 minutes after the examination time and uploaded within 15 minutes thereafter.
Question 1 (29 marks)

(a). A jointed rock sample is to be tested in a rock triaxial apparatus. The sample has a joint
oriented at 65° to the horizontal. The confining pressure (cell pressure) to be used is 2.2
MPa. Following strength properties can be assumed:
Intact rock : c' = 1.8 MPa ; Φ' = 36°
On the joint plane : c' = 0.8 MPa ; Φ' = 40°
It can be assumed that Mohr-Coulomb failure criterion is applicable to failure occurring
along the joint plane as well as through intact rock. According to the assumed rock
properties above, find the following:
(i). The mode of failure of the jointed rock sample when it is tested.
(ii). Axial stress at the failure of the sample.
[8 marks]

(b). A reinforced concrete arch dam is proposed to be built on a selected rock formation,
which is deemed suitable as far as the rock types (species) and topography are concerned.
The rock formation is jointed and consists of more than one rock type. The proposed dam
is as shown in Figure Q-1. It is necessary to classify the rock mass that would form
different parts of the foundation for the dam; also, in order to model the rock-dam
interaction using finite element analysis, it is necessary to obtain realistic deformation
modulus values for the rock mass.
Describe, with justification, the investigation/testing program you would carry out to
achieve the following outcomes (you may use diagrams in your answer):
(i). Classify different parts of the rock mass forming the dam foundation according to
a suitable Rock Mass Classification System. You may assume ‘different parts’ as the
left abutment, the right abutment and the foundation rock at the bottom of the valley
(see Figure Q-1).
[6 marks]
(ii). Obtain reasonable values for the deformation moduli of the rock mass for
modelling the structure using finite element analysis.
[5 marks]

(c). Briefly discuss the correlations between ‘void index of rocks’ and each of the following
rock characteristics (you may use diagrams):
(i). Geological age of rock.
(ii). Swelling strain of rock.
(iii). Seismic velocity of rock.
(iv). Crushing strength of rock.
[4 x 2.5 marks]

2
Figure Q-1

3
Question 2 (29 marks)

(a). An investigation of a rock mass revealed that three significant joint sets traverse the rock
mass with the orientations given in Table Q-2:
Table Q-2
Joint Set Average Dip Direction Average Dip Angle
No. (WCB from N)
1 56° 50°
2 132° 48°
3 209° 64°

A rock slope is cut in the rock mass (to facilitate a road) having a dip angle of (rock slope
angle) ψf = 60°, and a dip direction 102° (WCB from N). The friction angle on joint
planes of this rock mass has an average value of 26°. Assume that cohesion does not exist
on the joint planes.
(i). Plot the above information on a stereo plot and find the plunge and trend of the lines of
intersection between the above joint sets (consider the combinations of JS #1 and #2, JS
#2 and #3, and JS #1 and #3). Use a tracing paper to plot the information of the stereo-
plot. Attach the tracing paper to your answer script.
[9 marks]
(ii). Discuss the possibility for any types of rock slope instability that could take place on
this rock slope. Your answer must identify each type of rock slope failure that could take
place (e.g. wedge failure, plane failure, toppling failure, etc.), and the reasons for your
decision.
[5 marks]
(iii). For any one of the possible rock slope failure cases that you identified in (ii) above,
calculate the FOS against such rock slope failure assuming dry conditions and
cohesionless conditions along the respective joint planes. See the notes below:
Note 1: For a possible plane failure case, you may use the charts of Section 4.6.2 of the
Lecture Notes, assuming H = 30 m and z = 7.5 m.
Note 2: For a possible wedge failure case, you may use the Wedge Stability Charts for
Friction Only given in Section 4.7.3 of the Lecture Notes.
[5 marks]

(b). Discuss, by using suitable diagrams, the following with respect to remedial measures that
are applicable on specific rock slopes:
(i). Techniques applicable to de-pressurize rock slopes.
[5 marks]
(ii). Application of rock-bolts, and one type of mechanical anchor and one type of
chemical anchor used for tensioned rock bolts.
[5 marks]

4
Question 3 (21 marks)

(a). Laboratory radial percolation (permeability) tests can be used to determine permeability
of rock material. With respect to such testing, discuss the following (you may use
diagrams):
(i). Behaviour of rock with micro fissures in radial tests under compressive and tensile
stress fields.
[2.5 marks]
(ii). Behaviour of rock with spherical voids in radial tests under compressive and tensile
stress fields.
[2.5 marks]
(iii). The technique used to separate the effect of fluid pressure applied to cause
percolation through the rock material from the stress field applied to the rock material.
[3 marks]

(b). Assume that rock material at a certain point A located at a depth of 2400 m below surface
existed under a lithostatic stress state in the distant past. Also assume that the average
density of the rock material over this depth range was 26 kN/m3, Poisson’s ratio 0.25,
and that erosion had taken place over millions of years causing elastic unloading. If a
particular stress determination procedure establishes the current H/V (horizontal
normal stress to vertical normal stress) ratio at the above location A as 6.0, calculate the
height of overburden that had eroded away.
[4 marks]

(c). In a bore-hole pumping test (Lugeon Test), following data were recorded:
Pumping rate required to maintain a constant pressure in the test cavity = 0.52 m3/sec
Length of test cavity = 1.25 m
Total head in test cavity = 20 m
Diameter of bore-hole = 54 mm
Total head measured in a second bore-hole at a distance of 21 m from the test hole =
11.5m
(i). Clearly stating any other assumptions made, estimate the permeability of
discontinuities perpendicular to the bore-hole.
[3.5 marks]
(ii). If a second bore-hole is not available for the test, briefly explain how you would
estimate the above permeability value (do not make any computations).
[1.5 marks]
(d). Undisturbed rock core samples are necessary for laboratory tests such as tri-axial test to
determine shear strength parameters of rock material. However, it is difficult to obtain
undisturbed samples from a highly jointed rock-mass. In such cases, testing an equivalent
compacted rock-fill is justified. Describe, with the aid of sketches if necessary, how a
sample of compacted rock-fill can be prepared for this purpose; state all the precautions
to be observed during this procedure.
[4 marks]

5
Question 4 (21 marks)

(a). The load carrying capacity of a rock-socketed pier (pile) in compression is composed of
the load carried in side wall shear (of the socket wall) and load transferred to rock at the
base of the pier. Briefly explain the effect of the following factors on the load carried in
side wall shear (you may use diagrams):
(i). Geometry of the socket as defined by the length-to-diameter ratio.
(ii). Modulus of the rock, both around the socket and below the base, with respect to the
modulus of concrete in the pier.
(iii). Roughness of the socket wall, and the bonding between rock and concrete.
[6 marks]
(b). Briefly discuss the mechanisms by which tension foundations in rock resist applied uplift
loads.
[4 marks]
(c). Briefly discuss the aspects of foundation performance to be considered in the design of
surface footings on rock.
[4 marks]
(d). Describe one of the methods available for determination of stress in rock.
[4 marks]
(e). Draw a clear, labelled diagram to illustrate the typical failure mechanism for an end-
bearing pile, bearing at ground surface.
[3 marks]