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Surface settlement assessment due to tunnelling

(i) A single 10m diameter tunnel is to be constructed 28m below ground surface level within London Clay using a conventional shield. An overlying 3.5m diameter  tunnel is located 12m below ground level and at a right angles to the new tunnel.  In addition an important building (15m by 15m by 100m high) is located at  ground surface level directly above the centreline of the new tunnel. (N.B.  depths are given to tunnel axis level).

You have been asked to carry out a Stage 1 assessment in order to ascertain  whether there is any likelihood of movement occurring to the overlying structures. Given that the volume loss on similar projects is around 1.5%, calculate the maximum vertical displacements that will occur for each structure.

(ii) Describe the shape of the transverse and longitudinal surface settlement (i.e. vertical displacement) profiles likely to develop above a tunnel constructed in stiff clay. Provide a sketch of these profiles annotated with salient features;assume that the face of the tunnelling machine is directly below.

(iii) Explain briefly with the use of a sketch how the transverse and longitudinal surface settlement profiles would differ for an identical tunnel constructed in sand compare to that constructed in stiff clay.

Come up with a hypothetical circular, concrete, segmental tunnel driven in clay soils of a largely “greenfield” landscape. Assume that the tunnel is “wished in place” and hence construction sequencing is not considered and that it is a segmental lining consisting of a several segments per ring of 1m tunnel length. Following the example given in the lecture resources on moodle use the Curtis-Muir Wood Method to answer questions of Part 1 – 4. For this section, the report must contain:

1. Introduction: introducing your tunnel case, real or imagined.

2. Sensible values of properties assumed or used in the analysis for the ground and the  concrete.

3. Dimensions of the tunnel and location in the ground.

4. All the graphs and diagrams asked for.

5. Explanations, concisely written and brief.

Explain (with the aid of sketches) the sources of axial force within the tunnel lining when using the Curtis-Muir Wood method.

B. Calculate hoop thrust due to uniform ground pressure within the tunnel lining.

C. Calculate total hoop thrust within the tunnel lining for one half of the tunnel cross  section (between crown and invert). Use 45° intervals between calculated points.

D. Create a graph showing axial force versus angle. Plot results for both full shear interaction and zero shear interaction with the ground.

E. Draw an axial force diagram indicating points of maximum and minimum stress. Label the angle at which stated values occur.

Part 2 – Moments

F. Calculate moments due to tunnel lining deformation for one half the tunnel cross section (between crown and invert). Use 45° intervals between calculated points.

G. Create a graph showing bending moments versus angle. Plot results for both full shear interaction and zero shear interaction with the ground.

H. Draw a bending moment diagram indicating points of maximum and minimum  bending. Also label any points of contraflexure. Label the angle at which stated  values occur.

Part 3 – Deformations

I. Calculate the internal and external tunnel radii due to axial shortening at crown & axis level.

J. What are the displacements of the tunnel lining at crown and axis level due to tunnel lining deformation? Provide a sketch of the overall cross sectional deformation you would expect according to the Curtis-Muir Wood method.

K. What are the internal and external tunnel radii at crown and axis level following lining deformation and axial shortening?

Part 4 – Curtis-Muir Wood (General)

L. With reference to values calculated in parts 1 and 2; explain the difference between  full and zero shear interaction in terms of the soil and tunnel lining.

M. Explain why values calculated are not a true solution. Explain which sets of values calculated are upper and lower bound. What do you expect the true solution to be?

N. If the effective second moment of area for the segmental tunnel in the aforementioned scenario is 562.5x106mm4

, what is the thickness of the tunnel lining for a continuous concrete tunnel with four segments. Are results similar if a tunnel with less than four segments was used and why/why not?

O. Explain how you would expect bending moments and hoop forces to change if the elastic soil modulus was increased.