Question 1

Figure Q1 shows a propped embedded retaining wall, supported by an earth berm left on the excavation side of the wall.

(a).   Explain why in practice you might leave an earth berm against a wall during the excavation process.        [3 marks]

(b).   Using the water levels indicated in Figure Q1, propose a suitable long-term steady-state set of pore water pressures around the wall.                   [5 marks]

(c).   By  considering  the  limiting  equilibrium  of  a  series  of  potential passive sliding wedges extending from the bottom corner of the wall, determine the maximum horizontal force that the soil is able to provide to maintain the stability of the wall. The wall and berm geometry, and soil and wall properties are given in Figure Q1. You may solve the problem either graphically by means of force vector diagrams, or algebraically by resolving forces. You should apply a factor of safety of 1.25 to tanφ’ , but do not apply an overdig to the excavation level shown. State clearly any assumptions that you need to make.      [25 marks]

(d).   Calculate the earth and water pressures acting on the active side

of the wall using a lower bound solution. Take Ka  = 0.4491, which

has been determined for φ’design  (= tanφ’/1.25) and δ = ⅔φ’ . You

should factor the surcharge applied to the retained ground surface

by 1.3. Convert the pressure distributions obtained into total force reactions acting on the active side of the wall.       [6 marks]

Figure Q1. Propped embedded wall retaining a clayey silt, supported by an earth berm.

(e).   By taking moments around the top of the wall (where it meets the prop), show that the wall is approximately in moment equilibrium with the wall length of 10.7 m shown. State any assumptions that you need to make.                        [7 marks]

(f).    Calculate the prop load.                                                                [2 marks]

(g).   If  the  centreline of the  excavation is  9 m away from the wall,

explain qualitatively how that might change your answers to parts (c) and (e) above.        [3 marks]

(h).   Explain   qualitatively  how  you   might  test  the  stability  of  the proposed berm.         [3 marks]

[Total Q1 = 54 marks]

Question 2

A contractor needs to design a set of foundations to support a reinforced concrete  building.  As  the  building  does  not  follow  a  regular  plan geometry,  the  column  loads  that  the  foundations  must  carry  vary considerably, requiring a number of different foundation designs.

One foundation needs to carry a downward building column load of 500 kN.  The  short-term  ground  conditions,  assuming  the  silt  to  be undrained, are given in Figure Q2 below.

(a).   Determine the plan dimensions of a square concrete pad footing

required to carry the 500 kN applied column load. Assume that the

foundation will be a reinforced concrete pad 1 m deep, with the

founding plane at 1 m depth below ground level. You should apply

a factor of safety of 1.25 to tanφ’ . State any other assumptions that you need to make.          [14 marks]

(b).   Determine the minimum length of a single bored pile able to carry the 500 kN applied column load. Assume that the pile foundation will be constructed of reinforced concrete and is 0.5 min diameter. You should apply a factor of safety of 1.25 to tanφ’ and 1.4 to τu. Assume that the shear strength at the interface between the pile and the soil is given by δ = φ’ in effective stress conditions and τw = 0.5 × τu  in total stress undrained conditions. State any other assumptions that you need to make.                        [19 marks]

(c).   Comment on the answers that you have obtained for part (a) and part (b), in relation to the soil profile and soil strengths given in Figure Q2.                          [3 marks]

(d).   For the building described at the start of the question, explain why

it will be important to consider the Serviceability Limit State (SLS) of the foundations in the design process.       [3 marks]

Figure Q2. Ground profile.

(e).   Explain how a Continuous Flight Auger (CFA) pile is constructed.

Would  this  be  a  suitable  form  of  construction  for  the  pile considered in part (b)?         [7 marks]

[Total Q2 = 46 marks]

Foundation bearing equations:

Drained bearing capacity equations:

σ'f = Nq sq dq σ’0  + Ny  sy  dy  ry  [0.5yB – Δu]

Nq  = Kpeπtanφ'

Kp  = (1 + sinφ') / (1 – sinφ')

Ny  = (Nq – 1).tan(1.4φ')

sq  = sy  = 1 + 0.1Kp(B/L)

dq  = dy  = 1 + 0.1V(Kp) (D/B)

ry  = 1