Effects of tunnel construction on nearby pile foundations 5

The influence of pre-failure soil stiffness on the numerical analysis of tunnel construction.. Three-dimensional simulation of slurry shield tunneling, Geotechnical Aspects of Undergroun

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APPENDIX A PILE STIFFNESS FOR MRT NEL C704

First, the tangent modulus method proposed by Fellenius (1989) was used to derive the variation

of modulus with strain based on a pile load test carried out The pile tested had a similar concrete mix, reinforcement and installation procedure as other piles at the viaducts The pile was instrumented with thirty-two vibrating wire strain gauges and three telltale extensometers According to Fellenius (1989), the tangent modulus is represented as follow:-

B A

Where as the secant modulus to be used for converting strain to stress is as follow:-

B A

i.e initial tangent modulus (GPa) Figure A.1 shows a plot of the tangent modulus against the strain based on all the strain gauges and tell-tales in the pile By curve fitting, At is derived as -0.02 GPa/µε and B is within 30 to 50 GPa There seems to be a large variation between the upper and lower bounds This is likely to be due to the amount of shaft resistance mobilised at different depth The larger the shaft resistance, the lower the tangent modulus line (Fellenius, 2001) Another possibility could be due to the bored pile installation method The concrete was poured by tremie pipe and did not go through vibrating compaction, which leads to non-uniform property at different depth

approximate method by ACI (1989) as follows:

c

from cube strength Ultimately, the modulus was derived as 28.65GPa

Strain gauge and telltale data at 1st cycle

A B D E F G H I J K L M N O TT2 TT1

Figure A.1 Tangent modulus derived from a pile load test

-100 -50

SB

Tunnel springline

NB Tunnel

SB Tunnel

Tunnel springline

(a) (b) Figure A.2 Influence of (a) non-uniform strain distribution and (b) pile stiffness in the

interpretation of axial force in pile

APPENDIX B PILE MOMENT OF INERTIA FOR MRT NEL C704

interpretation of bending moment Depending on the significance of bending moment, the pile section could be in an un-cracked state (Ipile=Igross), fully cracked (Ipile=Icracked) or in between In order to investigate the appropriateness of the moment of inertia adopted, all the bending moments

z

I f

where fr is the modulus of rupture of concrete and is equal to 19 7 fc' (in kPa) as recommended

by ACI (1989), z is the distance from the centroid to the extreme fibre of the pile in tension (m)

and Igross is the gross moment of inertia (m4) which is calculated as

64

.D pile4

π

Figure B.1 shows the bending moment computed for all the 1.2m diameter instrumented piles

of the piles stayed within the cracked moment envelope after the two tunnels were driven However, there were some points within the piles where bending moment exceeded the cracked moment (particularly at Pier 11) It is observed that the bending moments exceeding the cracked moment were developed during the construction of the viaduct bridge (which exerted further loading on the piles)

Despite some points exceeding the cracked state, bending moment to be presented subsequently is

exceeding cracked moment would over-estimate the actual bending moment Further assessment

of the effective moment of inertia is not within the scope of this research

-1500 -1000 -500 0 500 1000 1500

-2000 -1000

1.6m

P2 P1

-3 -2

-1 0

P2 P1

-10 -5

0 Pile lateral deflection - transverse (mm)

Pile P1 (SDMCC) Pile P1 (NLES)

SB

1.6m

P2 P1

C.2 Comparison of pile responses between 3-D tunnel advancement and plane strain tunnel procedures

-10000 -5000

Plane strain tunnel (WL) With WL, Gmax/p'=800, VL=1%, Lp/Htun=3.0, Xpile/Dtun=1.0

-5 0

-5 0

Pile lateral deflection - transverse (mm)

With WL, Gmax/p'=800, VL=1%, Lp/Htun=3.0, Xpile/Dtun=1.0

Figure C.2 Comparison of pile responses with respect to different numerical simulation procedures (a) Pile axial force (b) Pile

settlement (c) Pile lateral deflection

APPENDIX D OTHER INFLUENCING FACTORS IN

PLANE STRAIN FE ANALYSIS

The calibration charts as presented in Chapter 6 only hold for the assumed cases particularly the

simulation These assumptions are further investigated here

D.1 Effect of soil model

To-date, there are probably hundreds of constitutive models available which allows the characteristics of soil to be modelled Therefore, it is impossible to investigate every one of the models At here, the commonly used ‘Mohr-Coulomb’ model is compared to the ‘Non-linear elastic’ model The tunnel-pile configuration and dimension remained the same in both analyses Total stress analysis was carried out with the Young’s modulus of soil, Eu of 30,000kPa, undrained

convergence plots for both the pile horizontal deflection and pile head settlement It can be observed that the modification factors differ up to two times for the two different models Strictly speaking, it is hard to justify the variation of modification factors for different soil models since the input parameters also play a role in determining the factors It is not within the scope of this study to quantify the effect of soil model

D.2 Effect of soil earth pressure at-rest

All the analyses that have been presented so far assumed the soil earth pressure at-rest, Ko of 1.0

than 1.0 in stiff over-consolidated soil Figure D.2 shows a comparison of convergence and the

corresponding modification factor between Ko of 1.0 and 1.5 in non-linear elastic model As can

pile horizontal deflection and pile head settlement However, it should be noted that the influence

of Ko parameter is highly dependent on the type of soil model adopted

Figure D.1 Influence of soil model on pile stiffness modification factor

0 50 100 150 200 250

2D response = 3D single pile response

2D response = 3D single pile response

0 50 100 150 200 250 300 350

Pile head sett (Mohr Coulomb)

D.3 Effect of twin tunnel simulation

The modification factor as investigated in Chapter 6 assumed a single tunnel simulation However,

in practice, there is a likelihood of encountering multiple tunnels interaction Study was also carried out to investigate the sensitivity of twin tunnels on the modification factor Two cases were simulated; single pile and one-row pile group Figures E.3a and b show respectively the typical 3-

D and 2-D mesh adopted for simulation of the twin tunnels which are located on each side of the single pile Equal distance between tunnel and pile was modelled on each side of the pile (i.e

described in Section 6.4.2 Figures D.4a and b compare the convergence obtained for pile horizontal deflection and pile head settlement respectively From the negligible differences, it can

be concluded that the modification factor is not affected by the twin tunnels in both single pile and one-row pile group