ECMM109
UNIVERSITY OF EXETER
COLLEGE OF ENGINEERING, MATHEMATICS
AND PHYSICAL SCIENCES
ENGINEERING
Advanced Geotechnical Engineering
Module Convenor: M. K. Wadee
You have 24 hours to complete this paper from the time of its release.
Intended Duration: TWO HOURS
May 2020
Answer ALL questions
Materials to be supplied:
Formula sheet (last page of the paper)
Graph paper
Approved calculators are permitted.
This is an OPEN BOOK examination.
ECMM109 1 TURN OVER
Question 1 (20 marks)
Consider the two-dimensional stress state measured on an in situ soil sample shown in
Figure Q1.
x
y
A
B
200
200
500
500
800 800
Figure Q1: Two-dimensional stress state in a soil. All stresses expressed in kN m 2
.
Answer the following multiple choice questions.
(a) The principal stresses are:
A. σ1 = 1330 kN m 2
and σ3 = -30 kN m 2
B. σ1 = 1150 kN m 2
and σ3 = 150 kN m 2
C. σ1 = 900 kN m 2
and σ3 = 400 kN m 2
D. σ1 = 800 kN m 2
and σ3 = 200 kN m 2
(5 marks)
(b) The major principal stress is orientated:
A. At an angle of 53.13
to the horizontal sloping up from left to right.
B. At an angle of 26.57
to the horizontal sloping up from left to right.
C. At an angle of 53.13
to the horizontal sloping up from right to left.
D. At an angle of 26.57
to the horizontal sloping up from right to left.
(5 marks)
(c) The direct stress along AB, which is orientated at 45
to the horizontal, is:
A. 530 kN m 2
B. 850 kN m 2
C. 250 kN m 2
D. 650 kN m 2
(5 marks)
(d) The magnitude of the shear stress along AB, which is orientated at 45
to the hori_xFFFE_zontal, is:
A. 400 kN m 2
B. 200 kN m 2
C. 90 kN m 2
D. 250 kN m 2
(5 marks)
ECMM109 2 CONTINUE
Question 2 (8 marks)
Briefly describe the following terms relating to Critical State Theory for saturated soils.
(a) Roscoe surface; (4 marks)
(b) Hvorslev surface. (4 marks)
Question 3 (12 marks)
With the help of sketches, briefly explain the differences in behaviour of a normally
consolidated clay and that of a heavily overconsolidated clay in triaxial testing in terms
of:
(a) the shape of stress-s
train curve; (4 marks)
(b) volume change behaviour in drained tests; (4 marks)
(c) change in pore pressure in undrained tests. (4 marks)
Question 4 (25 marks)
Figure Q4 shows the results from a conventional drained triaxial compression test. The
stress path starts from point P and follows points Q, R, S and T.
Figure Q4: (D. Muir Wood, 1990)
(a) What is your judgment on the stress history of this soil based on the observed
behaviour (7 marks)
(b) Explain in detail the stress paths in the (q, p′
), (v, p′
), (q, εq) and (v, εq) spaces
(Figure Q4(a), (b), (c) and (d)) and how they relate to one another. (18 marks)
NOTE: If needed, you may use the formula sheet given at the end of the paper.
ECMM109 3 TURN OVER
Question 5 (35 marks)
A soil has the following fundamental constants:
N = 2.75,
Γ = 2.6,
λ = 0.2,
κ = 0.1,
M = 0.9,
Gs = 2.6,
where N is the intercept of the isotropic normal compression line; Γ is the intercept of
the critical state line; λ is the gradient of the isotropic normal compression line; κ is the
gradient of the unloading-reloading line; all in v : ln p
′
space; M is the gradient of the
critical state line in q : p
′
space and Gs is the specific gravity of soil solid particles.
Two samples of this soil were consolidated to the same moisture content of 35% but
using different stress histories. Sample A was heavily overconsolidated and had a final
consolidation pressure of 40 kN m 2
. Sample B was normally consolidated.
Determine:
(a) the consolidation pressure for sample B; (10 marks)
(b) the overconsolidation pressure for sample A; (13 marks)
(c) the pore water pressure at failure in undrained triaxial tests on A and B. (12 marks)
Formula Sheet
Triaxial tests:
A = A0
1 εv
1 εa
.
The relationship between Γ and N:
Γ = N (λ κ) ln 2.
Elastic volumetric strain:
δεe
p = κ
δp′
vp′
.
Plastic volumetric strain:
δεp
p = (λ κ)
δp′
vp′
.
NCL:
v = N λ ln p
′
.
CSL:
v = Γ λ ln p
′
.
URL:
v = vκ κ ln p
′
.
END OF QUESTION PAPER
ECMM109 4