CVEN4202: Advanced Topics in Geotechnical Engineering
Weeks 11-12 Assignment
Question 1: stability of braced excavation in undrained clay (7.5 marks)
An undrained clay (γt ≠ 0,
cu
≠ 0) is excavated after sheet piles have been installed to a depth
D. When the excavated depth reaches H, failure occurs.
(a) Construct a compatible displacement increment diagram for the failure mechanism
assumed in Fig. 1.
(b) Express H as a function of B, D, γt,
cu given
the displacement increment diagram
drawn in (a).
optional: when
cu
varies linearly with depth according to
cu
=(1+ k·z)cu0 where k is a positive
constant and cu0 is the undrained shear strength at the ground surface (z=0), express k as a
function
of H, B, D, γt, cu0 given the displacement increment diagram
drawn
in (a).
Fig. 1: braced excavation failure mechanism
Question 2: bearing capacity of an inclinedly-loaded strip foundation (10 marks)
A dry sand foundation (φ’ ≠ 0, c’ ≠ 0) is loaded by a strip footing of width B. The vertical
load P and horizontal load T act at the
centre
of the footing (T/P=tan δ’).
Part A
(a) Construct a compatible displacement increment diagram for the failure mechanism
assumed in Fig. 2.1.
(b) For γ’ ≠ 0, express P/(c’B) and T/(c’B) as functions of B, δ’, α, γ’, c’, φ’ given the
displacement increment diagram
drawn
in (a). Determine δ’ when P/(c’B) =10, φ’
=30°, α =65°, c’/(γ’B) = 5.
Fig. 2.1: strip footing failure mechanism (γ’ ≠ 0)
Part B
(c) There is no relative displacement between region a and region b, and between region
b and region c in Fig. 2.2, construct a compatible displacement increment diagram for
the failure mechanism assumed in Fig 2.2. Show that α=π/4+φ’/2.
optional: assume weightless soil (γ’ = 0) and there is a uniform surcharge q applied on the
ground surface, express P/(c’B) and T/(c’B) as functions of B, δ’, β, q, c’, φ’ given the
displacement increment diagram drawn in (c). Determine δ’ when P/(c’B) =10, φ’ =30°,
β=90°, q =0 kPa.
Fig. 2.2: strip footing failure mechanism (γ’ = 0)
Notes: each optional question, correctly reasoned and answered, is awarded 2.5 bonus mark
which will be added on to the final course mark. Assignment is due 5 pm Thursday on 2nd
November 2017, submitted using the assignment submission box (AProfessor Russell) on
Level 5 of the Civil & Environmental Engineering building.