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1. (a) The slope shown in Figure 1 is part of the temporary works for the approaches for an immersed tube tunnel (a reinforced concrete box tunnel will be constructed in the excavation and then covered over). It failed shortly after construction on the circular arc indicated. Estimate the average undrained strength of the firm clay.
Properties of a sector of a circle are given on the data sheet.
[8 marks]
Figure 1

(b) The plan for the temporary works has been revised after the failure and the slope angle will be reduced to 45 . It will take nearly a year to construct the box tunnel before the excavation can be back-filled. Would you approve this revised plan (your answer must be supported by clear engineering reasoning)
[2 marks]

2. It has been proposed that the main foundation for a cable-stayed telecommunications mast is a single 12m long, 0.4m diameter driven circular steel pile (see Figure 2). The water table at the site varies seasonally from about 6m below the ground surface in summer to about 3m below the ground surface in winter.

(a)Giving your reasons, select the most appropriate water-table to be used to calculate the load capacity of this pile.
[1 mark]

(b)Based on the water-table selected in (a), calculate the ultimate axial load bearing capacity of this pile.
[8 marks]

(c)In windy conditions the mast will apply a horizontal load to the pile of 50 kN. What further design steps, if any, would you recommend
[1 marks]

Figure 2

3. A 1.4m x 1.2m rectangular pad foundation is shown in Figure 3.

(a)What is the maximum vertical load that this foundation can support
[3 marks]
(b)What will be the long-term settlement of the foundation if the load applied in service is 70kN Remember to explicitly justify any simplifying assumptions that are necessary to make this calculation (if needed you may assume that Ip = 0.88 for rectangular foundation).
[7 marks]
Figure 3. Pad foundation and associated soils data for Q3

4. Water is being pumped from reservoir to an end nozzle , where it will be discharged at atmospheric pressure. A pump is used to reach the required velocity at the end nozzle. As shown in Figure 4, the length of suction pipe, Pipe 1, is with a dimeter of . The delivery pipe, Pipe 2, is long with a diameter of . The internal roughness height of the pipe is . The local head losses at pipe entrance (from reservoir ) and pipe exit (at end nozzle ) can be calculated based on minor loss coefficients of and , respectively. The kinematic viscosity of water and density are and . The pump has an efficiency of . Calculate:

(a) The head produced by the pump ()
[6 marks]
(b) The pressure at pump suction side and comment on its value in this specific system
[2 marks]
(c) The electrical power required to be supplied to the pump
[2 marks]
You can use any appropriate method to estimate the friction factors. Make sure you show clearly which method you have used in your calculations.

Figure 4: Pipe and fittings arrangement for Question 4

5. (a) The two-reservoir system shown in Figure 5A consists of three concrete pipes with a constant friction factor of =0.024 for all pipes and an elevation difference of H = 50 m between two reservoir level.

(i)Calculate the flow rate between the two reservoirs (Ignore all minor losses)
[2 marks]
(ii)A new alternative solution is being considered to link the two reservoirs consisting of one pipe having a constant diameter. The flow rate calculated in (i) must be achieved and you may assume the friction factor is the same as in (i). A control valve will also be added to the system with a minor loss coefficient of . What is the diameter required for the pipe.
[4 marks]

Figure 5A: Reservoir and pipe arrangement for Question 5(a) (i) and (ii)

(b) Water flows in the system shown in Figure 5B. The pressure at is measured as . If the head loss between and is , calculate:
(i)The total flow rate in pipe 3 joining B-C
[2 marks]
(ii)The pressure at C.
[2 marks]
You may assume the friction factor, for all pipes, and the water density .
Ignore local losses at the pipe bends and junctions.

Figure 5B: Pipe network related to question 5(b)

6. (a) A local laboratory analysed a water sample and determined that it contained a Total solid (TS) content of 232 mg/L and a conductivity of 350 μS/cm. Calculate the Total Suspended Solid (TSS) content (mg/L) of the water sample.
[2 marks]
Note: The electrical conductivity and TDS of various types of water is shown in the Table.

(b) Determine the 1-day BOD and ultimate first-stage BOD for a wastewater whose 5-day 20°C BOD is 200 mg/L. The reaction constant k=0.23d-1. What would have been the 5-day BOD if the test had been conducted at 25°C.
(i)Determine the UBOD
(ii)Determine the 1-day BOD
(iii)Determine the 5-day BOD at 25 °C
[3 marks]
(c) A sample of water is found to contain the following dissolved salts in milligrams per litre Mg(HCO3)2 = 16.8, MgCl2 = 12.0, MgSO4 = 29.6 and NaCl = 5.0. Calculate temporary and permanent hardness of water for this sample.
[2 marks]
(d) The uptake for a water supply system is located at a location named X3 (see Figure 6 below); upstream of X3, there are two villages that discharge raw sewage at X1 and X2, and new wastewater treatment systems are needed in both villages in order to reduce the concentration of BOD. Calculate
(i)Current concentration of BOD at X3.
(ii)The required removal efficiency (% BOD removal) in the new wastewater treatment works (WWTW) to control BOD discharges at X1 and X2, so the BOD at X3 ≤ 20mg/L.
(iii)Plot the BOD versus distance for the two cases (before and after BOD removal).
[3 marks]

Figure 6

Geotechnics: FORMULA and DATA SHEET

Bearing capacity equation for a strip footing

qult = cNc + qNq +

Immediate settlement of a shallow foundation

i =

Shape factors for a shallow foundation

Shape of Base Sc Sq S
Continuous strip 1.0 1.0 1.0
Rectangle 1 + (B/L)(Nq/Nc) 1 + (B/L)sin 1 – 0.3 B/L
Square 1 + (B/L)(Nq/Nc) 1 + sin 0.7
Circle (B = diameter) 1 + (B/L)(Nq/Nc) 1 + sin 0.7
From “Decoding EuroCode 7” by Andrew Bond and Andrew Harris

Consolidation Ratio as a Function of Depth and Time Factor:
Uniform Initial Excess Pore Pressure

Average Consolidation ratio against Time Factor
Uniform Initial Excess Pore Pressure

Vertical Stress Increase Under Uniformly Loaded Footings

(a) Square Footing (b) Strip Footing

Newmark’s Chart for the Vertical Stress Increase under a Foundation

CRITICAL STATE SOIL MECHANICS – DEFINITIONS

Formula

V = 1+e

Equation of the Critical State Line is:
V = – ln p
where is the specific volume on the CSL when

Equation of the Isotropic Normal Compression Line:
V = V – ln p
where V is the specific volume on the INCL when

Equation of an Isotropic Unload –Reload Line:
V = V – ln p
where V is the specific volume on the URL when

Relationships between the gradients of the Isotropic Normal Compression Line and Unload_x001e_Reload Lines
– = V –

Equation of the Cam-Clay yield surface is:
= ln
where is the isotropic pre-compression stress