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CENV3020W1

SEMESTER 1 EXAMINATIONS 2019-20

TITLE:  GEOTECHNICAL ENGINEERING

Q.1

(i) Define the two bound theorems of plasticity. Describe how they might be used to find the true solution, and suggest advantages and limitations of both theorems. [6 marks]

(ii) Figure Q1(a) shows a large triangular mass of rock sitting on a thin clay filled fissure. The rock is believed to be on the verge of failure by sliding downwards along the clay in the fissure. By isolating the triangular mass of rock and considering it as a free body, determine the friction angle mobilised in the clay to just prevent the block sliding. [3 marks]

(iii) To stabilise the sliding block, it is proposed to drill a set of rock nails through the block at 2 m spacing along the slope and 20。to the horizontal, as shown in Figure Q1(b). The rock nails act in tension, to provide a force along the axis of the nail. Apply a design factor of safety of 1.25 to the value of tanφ’ determined for the clay  in part (ii). Using the factored strength for the clay, determine the minimum tensile force that a nail needs to provide to the triangular mass of rock to maintain it’s stability.          [13 marks]

[Q1 Total marks = 22]

Fig. Q1 (a) Marginally stable triangular mass of rock sitting on a thin clay seam along which it can slide; (b) Arrangement for nails used to stabilise the mass of rock.

Q.2

(i) Describe the purpose and need for application of a factor of safety in geotechnical engineering calculations. In your answer, consider both the ultimate limit state, and serviceability limit state. [6 marks]

Figure Q2 shows a proposed gravity retaining wall to be constructed within a soft clay soil. The figure gives values for the soil and wall properties, and indicates the long-term groundwater conditions around the wall. Figure Q2 is given at the end of the question, over the page.

(ii) Using a lower bound analysis, show that in short-term undrained conditions, a fully flooded tension crack will form down the full depth of the back of the retaining wall. (Ignore the water table marked on Figure Q2, and assume that the crack will flood right up to the retained ground surface level). In your calculation, apply a factor of safety of 1.4 to τu, and assume that the unit weight of water is 10 kN/m3. Calculate the water pressure reaction acting onto the back of the retaining wall. [5 marks]

(iii) Determine the horizontal earth and water pressures acting onto the back of the wall in long-term effective stress conditions. Use a lower bound analysis, assuming that the active earth pressure coefficient, Ka, is equal to 0.491, which is consistent with application of a factor of safety of 1.25 to tanφ’, and δ = φ’ at the soil-wall interface. Assume that water pressures are hydrostatic behind the wall, below the long-term water table shown in Figure Q2.

Combine the reactions that you calculate for the soil and water pressures to give a single reaction acting onto the back of the  retaining wall. [7 marks]

(iv) State which of your answers from part (ii) or (iii) is the more critical loading for stability of the wall. [1 mark]

(v) Taking your answers from part (iii), draw a free body diagram for the wall. Assume that any reactions on the base of the wall will also be in long-term effective stress conditions. Where they are already known, mark onto your free body diagram both the value of the forces acting on the wall and their line of action on the structure. [11 marks]

(iv) Using the free body diagram in part (v), determine whether the wall is safe, or will fail, for both sliding and toppling. Where appropriate, you should assume that the soil-wall interface has friction angle δ = φ’, and apply a factor of safety of 1.25 to tanδ . [11 marks]

(v) If the wall design is inadequate in either toppling or sliding, suggest three things that could be changed to try to improve its stability. [3 marks]

[Q2 Total marks = 44]

Fig. Q2 Cross-section through a concrete gravity retaining wall

Q.3

(i) Explain the terms ‘active’ and ‘passive’ in the context of a shallow foundation. [3 marks]

A high-rise building has major internal columns that provide a factored load of 2 MN at ground level. A foundation is required to transfer the load into the soil. The soil and groundwater properties, including the unit weight, strength, and in situ stress state for the site are given in Figure Q3.

(ii) Calculate the plan dimensions of a square pad footing required to carry a 2 MN column load in the short-term, assuming that the footing is founded 2 m below ground level. Apply a factor of safety of 1.4 to the undrained shear strength of the soil, τu. The equation for the bearing capacity of an undrained total stress soil is given below.   [8 marks]

Undrained bearing capacity equations:

(σf – σ0) = (Nc  sc  dc) τu

Nc  = 5.14

sc  = 1+ 0.2(B/L)

dc  = 1 + 0.23 x V[D/B] up to a maximum of 1.46 (D/B = 4)

B = Width of foundation

D = Depth of foundation

L = Length of foundation

(iii) The pad footing is considered to use too much concrete in construction, and the contractor proposes to use instead a 600 mm diameter bored concrete pile. Calculate the length of pile required to carry a 2 MN column load, in short-term conditions. Apply a factor of safety of 1.4 to the undrained shear strength of the soil, τu, and assume that at the interface between the pile and soil the adhesion, τw  = 0.5 τu,design. Where the pile passes through a drained soil, apply a factor of safety of 1.25 to tanφ’ , and assume that at the interface between the pile and soil δ = 0.67φ’design. Finally, assume that the unit weight of concrete, gc  = 24 kN/m3 . [21 marks]

(iv) Suggest two other checks that you would need to carry out to complete the design of the pile foundation. [2 marks]

[Q3 Total marks = 34]

Figure Q3. Soil conditions at the site.