robust geotechnical design of shield tunnelshsein/wp-content/uploads/2017/01/robust... · robust...

Hsein Juang

Glenn Professor, Clemson University

Tongji University

August 4, 2015

Robust Geotechnical Design of

Shield Tunnels

Acknowledgments Robust design research at Clemson

Sponsors: National Science Foundation and Glenn Department of Civil Engineering, Clemson University

Investigators: Hsein Juang, Sez Atamturktur

Ph.D. students: Jerry Luo, Zhifeng Liu, Lei Wang, Wenping Gong, Sara Khoshnevisan, Andrew Brownlow

Collaborators: Hongwei Huang & Jason Zhang (Tongji Univ., Shanghai); Hsii-Sheng Hsieh (TFEC, Taipei), Gordon Denby (GeoEngineers, Seattle), 2

Outline of Presentation

1. Introduction

2. Robust Geotechnical Design (RGD)

Methodology - A New Design Perspective

3. Application of Robust Geotechnical

Design (RGD) Methodology - Shield Tunnels

4. Summary and Concluding Remarks

3

1. Introduction –

What is Robust Design?

4

What is Robust Design? Robust design aims to make a product insensitive to “hard-to-

control” input parameters (called “noise factors”) by carefully

adjusting “easy-to-control” input parameters (called “design

parameters”). -- Taguchi (1986)

5

Wayne Taylor

http://www.va

riation.com/te

chlib/val-

1.html

Transforming Robust Design

Concept into a Novel Geotechnical

Design Tool

6

Geotechnical Design Methodologies

Factor of Safety (FS)-Based Approach (Coping with uncertainties by means of experience and

engineering judgment)

Reliability-Based Design (RBD) (Incorporating uncertainties explicitly in the analysis;

however, difficult to characterize uncertainties of soil

parameters, model errors & construction variation)

Load and Resistance Factor Design (LRFD) (Current trend; however, uniform risk unattainable with

single resistance factors for each analysis model with

wide ranges of COVs in the input soil parameters)

7

Robust Geotechnical Design

Offers a new design perspective in the field

of geotechnical engineering

Is not to replace existing design methods

(FS-based design, RBD or LRFD approach)

Complements traditional design approaches

(FS-based approach, RBD, or LRFD)

8

2. Robust Geotechnical Design

(RGD) Methodology

9


Seeks an optimal design that is insensitive to, or robust against, variation in noise factors such as uncertain soil parameters, model errors, and construction variation.

Considers simultaneously safety, robustness, and cost by means of optimization.

10

Key Concepts in RGD

A) Design parameters (easy to control) versus noise factors (hard to control)

B) Measure of design robustness

C) Optimization and Pareto front

11

A) Design parameters & Noise factors (Using the design of shield tunnels as an example)

Design parameters: Segment thickness (t)

Segment reinforcement ratio ()

Steel bolt diameter (Dj)

12

Noise factors: Soil parameters (Ks, c, )

Ground water table (HGWT)

Ground surcharge (q0)

R

1°

y

x

p1

p3 + p4

ph

p6

p2

p5

p3

q0

H

HG

WT

Groundwater table

B) Measures of design robustness

Variation of system response (in terms of

factor of safety, failure probability,

deformation)

Signal-to-Noise Ratio (SNR)

Feasibility Robustness

13

Find d to optimize: [C(d), R(d,)]

Subject to: gi(d,) ≤ 0, i = 1,..,n

d - design parameters;

- noise factors;

C - cost;

R - robustness measure;

g – safety constraint.

C) Robust design optimization

14

Illustration of Pareto front in 2-D

15

Optimization may not yield a single best design with respect to all objectives.

Rather, a set of “non-dominated” designs may be obtained. This set of designs collectively forms a Pareto front.

Infeasible domain

Pareto front

Ob

ject

ive

2,

f2(d

)

Objective 1, f1(d)

Feasible domain

Knee point

Utopia point

3. Application of


(RGD) Methodology

16

Summary of RGD Examples

Example

No.

System System

response

Noise factors Robustness

measure

#1 Braced

Excavation

Deformation Soil parameters

(su, kh)

Variation of

deformation

#2 Soil Slope Factor of

Safety

Soil parameters

(c, , ru)

Signal to noise ratio

(SNR) of factor of

safety

#3 Drilled

Shaft

Failure

Probability

Statistics of soil

parameters (, K0)

Variation of failure

probability and

feasibility robustness

#4 Shallow

Foundation

Failure

Probability

Statistics of soil

parameter and model

parameters

Variation of failure

probability and

feasibility robustness

#5 Shield

Tunnel

Factor of

Safety

Soil parameters (Ks,

c’, ’), water table

(HGWT), and

surcharge (q0)

Signal to noise ratio

(SNR) of factor of

safety

Example #5 – RGD of Shield Tunnels (1)

Noise Factors: Ks 3500 ~ 15000 kN/m3

c 0 ~ 15 kN/m2

30 ~ 35.3

HGWT 0.5 ~ 2.0 m

q0 0 ~ 15 kN/m2

Design Parameters: t 0.2 ~ 0.5 m

0.5 ~ 4.0%

Dj 10 ~ 50 mm

Solution Model: Lee’s analytical solution (2001)

- Force method-based solution

18

R

1°

y

x

p1

p3 + p4

ph

p6

p2

p5

p3

q0

H

HG

WT

Groundwater table

(Fuzzy sets are

used to model

noise factors)

Design example – One tunnel segment (Gong et al. 2014a)

Gong, W., Wang, L., Juang, C. H.*, Zhang, J., & Huang, H. (2014a). Robust geotechnical design of shield-

driven tunnels. Computers and Geotechnics, 56, 191-201.

A few words on the selection of analysis model

– higher sophistication equals better model?

“Everything should be made as simple as possible

but no simpler” (Einstein)

When selecting a numerical model for a geotechnical

problem, robustness of the model may be as

important as fidelity of the model. This is especially

critical when the model is to be used in a robust

design framework.

19

(x)

x

1.0

0.0a bm

i

ix

ix

i-cut interval

(Fs)

Fs

1.0

0.0A B

Ci-level

Fsia

Fsia

i

Fuzzy Sets Theory

20

For a system with fuzzy sets as inputs, the system

response (i.e., factor of safety Fs) will be a fuzzy

set. Then, the uncertainty propagation is realized

through vertex method.

Fuzzy input

(input is described as “a ~ b”)

Fuzzy output

(output is described as “A ~ B”)

Find: (t, , Dj) Subjected to: tl t tu; l u; Djl Dj Dju;

Objective: Maximizing the robustness index of ULS, SNR1

Maximizing the robustness index of SLS, SNR2

Minimizing the cost, C (t, , Dj)

21

Multi-objective Optimization Formulation

(design parameters)

(safety)

(robustness)

(cost)

(local practice)

Note: the reliability index and signal-to-noise ratio of

tunnel performance is computed with the fuzzy outputs

Pareto Front for Shield Tunnels (Only non-dominated designs that satisfy all safety constraints

are shown)

22

3D Pareto front

1015

2025

30

1015

2025

300

2000

4000

6000

Robustness (SNR1)Robustness (SNR

2)

Co

st (

C:

US

D)

Identified knee point

t = 288.1 mm

= 1.16 %

Dj = 49.2 mm

Corresponding objectives SNR1 = 10.793

SNR2 = 16.070

C = 1234.2 USD


are shown)

23

3D Pareto front

1015

2025

30

1015

2025

300

2000

4000

6000

Robustness (SNR1)Robustness (SNR

2)

Co

st (

C:

US

D)

0 1000 2000 3000 4000 5000 600010

15

20

25

30

SNR1

SNR2

Ro

bu

stn

ess

(SN

R1,

SN

R2)

Cost (C: USD)

2D Pareto front

Identified knee point

t = 288.1 mm

= 1.16 %

Dj = 49.2 mm

Corresponding objectives SNR1 = 10.793

SNR2 = 16.070

C = 1234.2 USD

24

Summary of RGD of Shield Tunnels

(one tunnel segment)

A fuzzy sets-based RGD method is advanced

and shown effective in producing a robust

design of shield tunnel segment design.

The Pareto front obtained from RGD shows the

tradeoff between design robustness and cost

efficiency.

The knee point on the Pareto front can be

selected as the best compromised design.

Example #5 – RGD of Shield Tunnels (2) Design example – Tunnel longitudinal structure (Gong et al. 2015)

25 Gong, W., Huang, H., Juang, C.H*, Atamturktur, S., and Brownlow, A. (2015). “Improved shield tunnel design

methodology incorporating design robustness.” Canadian Geotechnical Journal.

Seattle Tunnel

Longitudinal length: 2.8 km

Diameter: 17.45 m Shanghai Yangtze River Tunnel

Longitudinal length: 6.8 km

Diameter: 15.43 m

0 50 100 150 200 250 3000

4

8

12

16

20

Eff

ecti

ve

coh

esio

n (

c, k

N/m

2)

Longitudinal coordinate (x, m)

Example #5 – RGD of Shield Tunnels (2) Design example – Tunnel longitudinal structure

26

0 50 100 150 200 250 3000

20

40

60

80

100

Gro

un

d s

tiff

nes

s (k

v,

10

3k

N/m

3)


0 50 100 150 200 250 3000

3

6

9

12

15

Gro

un

d s

tiff

nes

s (k

h,

10

3k

N/m

3)


0 50 100 150 200 250 30030

31

32

33

34

35

Eff

ecti

ve

fric

tio

n a

ng

le (, )


0 50 100 150 200 250 3000.0

0.5

1.0

1.5

2.0

2.5

Gro

un

d w

ater

tab

le (

Hw,

m)


0 50 100 150 200 250 3000

5

10

15

20

25

Gro

un

d s

urc

har

ge

(q0,

kN

/m2)


Effective friction angle Ground water table Ground surcharge

Vertical ground stiffness Horizontal ground stiffness Effective cohesion

Characterization of the Longitudinal

Variation of Input Parameters

Noise factors Mean Coefficient

of variation

Scale of

fluctuation Distribution

Vertical ground stiffness of the

ground under the tunnel

(kv, kN/m3)

33000 0.500 50 Lognormal

Effective cohesion of soil

(c, kN/m2) 7.5 0.333 50 Lognormal

Effective friction angle of soil

(, ) 32.65 0.027 50 Lognormal

Horizontal ground stiffness of

soil (kh, kN/m3) 9250 0.207 50 Lognormal

Ground water table (HW, m) 1.25 0.200 50 Lognormal

Ground surcharge (q0, kN/m2) 10 0.333 50 Lognormal 27

Huang, H., Gong, W., Khoshnevisan, S., Juang, C.H.*, Zhang, D., & Wang, L. (2015). “Simplified procedure for

finite element analysis of the longitudinal performance of shield tunnels considering spatial soil variability in

longitudinal direction.” Computers and Geotechnics, 64, 132-145

Improved Model for Shield Tunnel

Performance Analysis

Generate tunnel design parameters

with MCS that considers the longitudinal variation

Start

Winkler elastic foundation theory-based

FEM analysis of tunnel longitudinal performance

(i.e., settlement, rotation, moment, and shear force)

Force method-based analytical analysis

of the performance of tunnel segmental ring

(i.e., structure safety and serviceability)

All segment

rings are completed?

Required MCS

runs are completed?

End

Yes

Yes

No

(Inner loop)

No

(Outer loop)

Step 1: generate input parameters

in the longitudinal domain with MCS

Step 2: 1-D FEM analysis of tunnel

longitudinal behavior (Huang et al. 2015)

Step 3: 2-D analytical solution of the

performance of one segment ring (Gong et al. 2015)

Step 4: repeat Step 3 for each and

every segment ring (inner loop)

Step 5: repeat Step 1, Step 2, Step

3 and Step 4 until a converged

solution is achieved (outer loop)

Gong, W., Juang, C. H.*, Huang, H., Zhang, J., & Luo, Z. (2015). Improved analytical model for circumferential

behavior of jointed shield tunnels considering the longitudinal differential settlement. Tunnelling and

Underground Space Technology, 45, 153-165.

28

1 1.5 2 2.5 30

2000

4000

6000

8000

Factor of safety with respect to structure safety (Fs1)

Fre

qu

ency

co

un

ts

Histogram

Normal fitting

1 1.5 2 2.5 30

2000

4000

6000

8000

Factor of safety with respect to serviceability (Fs2)

Fre

qu

ency

co

un

ts

Histogram

Normal fitting

Effectiveness of the Improved Model of

Shield Tunnels (1)

Existing method (not consider the longitudinal variation of input parameters)

Failure probability with respect to structure safety: 4.010-5

Failure probability with respect to serviceability: 0

Not consistent with long term structure health

monitoring data (in Shanghai)

29

Effectiveness of the Improved Model of

Shield Tunnels (2)

Improved method (consider the longitudinal variation of input parameters)

Failure probability with respect to structure safety: 2.1410-1

Failure probability with respect to serviceability: 2.98 10-2

Consistent with long term structure health

monitoring data (in Shanghai)

0 0.1 0.2 0.3 0.40

50

100

150

200

Failure probability with respect to structure safety (Pf1

)

Fre

qu

ency

co

un

ts

Histogram

Normal fitting

0 0.1 0.2 0.3 0.40

50

100

150

200

Fre

qu

ency

co

un

ts

Failure probability with respect to serviceability (Pf2

)

Histogram

Normal fitting

30

Signal-to-Noise Ratio (SNR)-Based

Design Robustness

7 8 9 10 11 12 13 14 150

50

100

150

SNR with respect to structure safety (SNR1)

Fre

qu

ency

co

un

ts

Histogram

Normal fittingR

1

Distribution of SNR1

1 2 3 4 5 6 7 8 90

50

100

150

SNR with respect to serviceability (SNR2)

Fre

qu

ency

co

un

ts

Histogram

Normal fittingR

2

Distribution of SNR2

SNR SNR2R

Due to the longitudinal variation of input parameters (or noise

factors), different tunnel segments yield different signal-to-

noise ratios. Then, a lower bound of SNR is defined as the

robustness measure:

31

Optimization Setting of the Design Space

Easy-to-control design

parameter Possible value

Segment thickness (t: m) {0.25, 0.30, 0.35, 0.40, 0.45}

Steel reinforcement ratio of

tunnel segment (: %) {0.5, 1.0, 1.5, 2.0}

Bolt diameter of the

circumferential joints (Dc: mm) {20, 25, 30, 35, 40}

Bolt diameter of the longitudinal

joints (Dl: mm) {20, 25, 30, 35, 40}

Note: 1) Bolt diameter of the longitudinal joints cannot be optimized

in the robust design of one tunnel segment.

2) While the discrete design space is used is this example, the

continuous design space can also be used. 32


are shown)

3D Pareto front: 3D surface

05

1015

24

68

10200

400

600

800

Design robustness (R1)Design robustness (R

2)

Co

st (

C,

10

00

US

D)

Non-dominated designs

Knee point

Real-world design Identified knee point

t = 350 mm

= 0.5 %

Dc = 20 mm

Dl = 30 mm

33

Effectiveness of the Robust Design

Optimization Results

Designs

Easy-to-control design

parameters (d)

Design

feasibility

Tunnel

performance Design objectives

t

(m)

(%)

Dc

(mm)

Dl

(mm) f1 f2 Fs1 Fs1

C

(1000

USD)

R1 R2

Knee

point 0.35 0.5 20 30 0.9607 0.9033 1.90 1.80 309.57 9.59 4.89

Real-

world

design

0.35 0.5 30 30 0.7846 0.9695 1.39 2.50 316.67 8.78 2.31

1 1

2 2

Pr Fs 1.0

Pr Fs 1.0

f

f

1 SNR1 SNR1

2 SNR2 SNR2

2

2

R

R

34

35

Summary of RGD of Shield Tunnels

(one tunnel longitudinal structure)

An improved model of shield tunnel performance

was advanced, in which the longitudinal variation

of input parameters can be explicitly considered.

The robust design methodology of shield tunnels

was developed, in which the robustness of the

shield tunnel performance against the longitudinal

variation of input parameters was enhanced.

4. Concluding Remarks

36

Concluding Remarks

Robust Geotechnical Design, a new design

paradigm, has been demonstrated as an effective

tool to obtain optimal designs that are robust

against variation in noise factors (e.g., uncertain

geotechnical parameters).

RGD with multi-objective optimization can consider

safety, cost, and robustness simultaneously and

effectively.

RGD has been shown as an effective design tool

for multiple geotechnical problems.

37

38 4th ISGSR, December 2013

Thank You！

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