Load and Resistance Factor Design Considering Design ...hsein/wp-content/uploads/2017/01/Load... · Load and Resistance Factor Design Considering Design Robustness: R-LRFD ... Load

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Load and Resistance Factor Design Considering Design Robustness: R-LRFD

Hsein Juang, PhD, PE, F.ASCE

Glenn Professor

Glenn Department of Civil Engineering

Clemson University

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Outline

1. Background (Robust design)

2. Methodology of R-LRFD (Robust Load and Resistance Factor Design)

3. Illustrative Example: Drilled Shaft in Clay

4. Conclusions

3

Outline

1. Background

2. Methodology of R-LRFD


4. Conclusions

4

Background

Robust design aims to make a product or design insensitive to

“hard-to-control” input parameters q (called “noise factors”) by

carefully adjusting “easy-to-control” input parameters d (called

“design parameters”). --- Taguchi (1986)

Robust design concept

Wayne Taylor

http://www.va

riation.com/te

chlib/val-

1.html

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Background

Taguchi method (originated in Industrial Engrg)

(a) (b)

Fre

que

ncy o

f O

ccurr

ence

response Target Value

Fre

que

ncy o

f O

ccurr

ence

response Target Value

Minimizing variability

Moving mean

1.Reduce variance of system response

2.Bring mean of system response to target

6

Background

Transforming Robust Design Concept

into a Novel Geotechnical Design Tool

(National Science Foundation

grant No. CMMI-1200117)

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Background

Factor of safety (FS)-based approach (Coping with uncertainties by means of experience and

engineering judgment; “calculated risk” concept)

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 COV in the input soil parameters)

Current geotechnical design methods

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Background

Offers a new design perspective in the field of

geotechnical engineering

It is not to replace existing design methods (FS-

based design, RBD, or LRFD approach)

Complements traditional design approaches (FS-

based approach, RBD, or LRFD approach)

Robust geotechnical design (RGD)

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Outline

1. Background



4. Conclusions

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Methodology of R-LRFD

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

Considers simultaneously safety, robustness, and cost by means of optimization, it is a multi-objective optimization problem.

Load and Resistance Factor Design Considering Design Robustness: R-LRFD

(Robust design plus LRFD)

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Key concepts in R-LRFD

Design parameters d (easy-to-control) versus noise factors q (hard-to-control)

Measure of design robustness

Optimization, Pareto front, and knee point

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Design parameters versus noise factors (1)

Easy-to-control design parameters

o Geometry parameters

o Construction parameters

Hard-to-control noise factors

o Geotechnical parameters

o Loading conditions

o Model parameters/model errors

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Design parameters versus noise factors (2)

Design parameters:

Wall length (L), Wall

thickness (t), Vertical

spacing of the struts (S),

Strut stiffness (EA)

GL -2 m-1 m

-7 mGL -8 m

GL -4 m-3 m

GL -6 m-5 m

GL -10 m

Clay

Clay

Noise factors: Undrained

shear strength ( ),

horizontal subgrade reaction

( ), and surcharge

behind the wall (qs)

(Using diaphragm-wall supported excavation as an example)

h vk

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Measure of design robustness in R-LRFD (slide 1)

The system performance, in the context of LRFD approach,

may be presented as:

where R(d, kθ) and S(d, kθ) are the resistance term and load

term, respectively; R and S are the resistance factor and load

factor, respectively; and, kθ are the characteristic values of

noise factors θ.

( , ) ( , ) ( , )R Sf R S d k d k d kq q q

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Intuitively, the design robustness or the sensitivity of the

system response to the noise factors can be mathematically

measured using its gradient , expressed as follows:

1 2

( , ) ( , ) ( , )( , ) , , ,

n

f f ff

k k kq q q

k k k

d k d k d kd k

q q q

q q qq

q q q

( , )f d kq

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f (d1,q )

Sensitive

Design response, f (d,q )

Noise factors, q

f (d2,q )Robust

Lower vs. higher gradient


Lower degree of design

robustness, signaled by

higher gradient

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Sensitivity index (SI) of the system response to the noise

factors is defined based on the gradient ,

A higher SI value signals a lower degree of design

robustness, as it would suggest a greater relative variation

of the system response due to the variation in the noise

factors.

31 2

1 2

( , ) ( , ) ( , ), , ,

( , ) ( , ) ( , )n

kk kf f f

f k f k f k

qq q

q q q

k k k

d k d k d kJ

d k d k d kq q q

q q q

q q qq q q

TSI J JJ

( , )f d kq

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Optimization, Pareto front (Slide 1)

Find d to optimize: [C(d), SI(d,q)]

Subject to: gi(d,q) ≤ 0, i = 1,..,m

d - design parameters;

q - noise factors;

C - cost;

SI - robustness measure;

g - design constraint.

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Optimization, Pareto front (Slide 2)

Find: (Design parameters)

Subject to: (Design space)

( , ) 0 ( )

Objectives: Min ( ) (Sensitivity index)

Min ( ) (Cos

Design constrai

t

t

)

n f >

SI

C

d

d S

d kq

(In the context of R-LRFD)

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(Slide 3)

Multi-objective 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.

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Optimization, Pareto front, and knee point (4) If no preference is assigned in the robust design optimization, the knee point on the Pareto front that yields the best compromised solution can be selected as most preferred design in the design space.

Infeasible domain

Pareto front

Ob

ject

ive

2,

f2(d

)

Objective 1, f1(d)

Feasible domain

Knee point

Utopia point

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Outline

1. Background



4. Conclusions

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Illustrative Example: Drilled Shaft in Clay

Schematic diagram of a drilled shaft in clay (after ETC10)

Design parameters:

Pile diameter (D) and pile

length (L)

Noise factors: Onsite diameter (DT), onsite

length (LT), normalized

undrained shear strength (cn

= cu/z), dead load (Fd), and

live load (Fl).

System response of concern:

The ultimate limit state (ULS)

performance (Orr et al. 2011)

Fd + Fl

L = ?

D = 0.45 m

Stiff clay

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Characterization of noise factors in R-LRFD (#1) If a noise factor follows the lognormal distribution, the corresponding characteristic value can be estimated as: where is the characteristic value of ith noise factor; and

are the mean and coefficient of variation (COV) of ith noise

factor, respectively. Note that the number of 1.645 is adopted

in above Equation to ensure that there is 95% likelihood of ith

noise factor not greater than (for the load term) or less than (for

the resistance term) the characteristic value of .

2 21exp ln ln 1 1.645 ln 1

2i i i ikq q q q

ikq

ikq iq

iq

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Characterization of noise factors in R-LRFD (#2)

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Characterization of noise factors in R-LRFD (#2)

Other assumption can be made

Characterized using test data

Specified in ETC 10

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Construct the system response in R-LRFD (#1)

The system performance in the context of R-LRFD, in terms

of ULS performance, can be presented as:

where 1, 2, 3, 4, 5, 6, and 7 are the partial factors on

undrained shear strength along the pile length (cu1), undrained

shear strength at the pile base (cu2), slide resistance (Qs), end

resistance (Qb), selected geotechnical model (Equation 9), dead

load (Fd), and live load (Fl), respectively.

T

T u1 1 b c u2 205 d 6 l 7

3 4

( , )

L

D c dz A N cf F F

d kq

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Illustrative example

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Results of the R-LRFD optimization

18 19 20 21 22 23 24 250

50

100

150

200

250

Sen

siti

vit

y i

nd

ex,

SI

Cost, C (m)

Pareto front

Least cost Preferred design

Knee point

Most robust

(For a given design space S1, where D = 0.45 m and L

{10.0 m, 10.3 m, 10.6 m, …, 24.7 m, 25.0 m})

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The optimization results of R-LRFD

18 19 20 21 22 23 24 250

50

100

150

200

250

Sen

siti

vit

y i

nd

ex,

SI

Cost, C (m)

Pareto front

Least cost Preferred design

Knee point

Most robust

(For a given design space S1, where D = 0.45 m and L

{10.0 m, 10.3 m, 10.6 m, …, 24.7 m, 25.0 m})

, (kN)

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Effect of COV of input noise factors

0 5 10 15 20 25 300.0

0.2

0.4

0.6

0.8

1.0

Fea

sib

ilit

y,

Pr [

f (

d,k

q)]

Coefficient of variation of kq, COV(%)

Least cost design

Knee point

Most robust design

Least-cost design cannot withstand the variation; most robust design would still be feasible even at high COV but is costly.

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Effect of selected design space

18 19 20 21 22 23 24 250

50

100

150

200

250

Sen

siti

vit

y i

ndex

, SI

Cost, C (m)

Pareto front in S1

Knee point in S1

(D = 0.45 m, L = 19.5 m)

Knee point in S2

(D = 0.45 m, L = 19.34 m)

Pareto front in S2

18 20 22 24 26 28 300

50

100

150

200

250

Knee point in S1

(D = 0.45 m, L = 19.5 m)

Sen

siti

vit

y i

ndex

, SI

Cost, C (m)

Pareto front in S1

Pareto front in S3

Knee point in S3

(D = 0.45 m, L = 19.7 m)

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18 19 20 21 22 23 24 250

50

100

150

200

250

Sen

siti

vit

y i

ndex

, SI

Cost, C (m)

Pareto front in S1

Knee point in S1

(D = 0.45 m, L = 19.5 m)

Knee point in S2

(D = 0.45 m, L = 19.34 m)

Pareto front in S2

18 20 22 24 26 28 300

50

100

150

200

250

Knee point in S1

(D = 0.45 m, L = 19.5 m)

Sen

siti

vit

y i

ndex

, SI

Cost, C (m)

Pareto front in S1

Pareto front in S3

Knee point in S3

(D = 0.45 m, L = 19.7 m)

Effect of selected design space

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Outline

1. Background



4. Conclusions

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Conclusions

R-LRFD, 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 soil parameters,

model errors, and construction variation).

R-LRFD consider safety, cost, and robustness simultaneously

and is shown as an effective tool.

Pareto front and knee point concepts can aid in making

informed decision in the design.

The proposed gradient-based robust design methodology

complements all existing design methods, including the FS-

based approach, RBD, or LRFD approach.

Selected papers on robust design

*Gong, W., *Khoshnevisan, S., Juang, C.H., “Gradient-based design robustness

measure for robust geotechnical design,” Canadian Geotechnical Journal, 2014.

*Gong, W., *Wang, L., *Khoshnevisan, S., Juang, C.H., Huang, H., and Zhang, J.,

“Robust geotechnical design of earth slopes using fuzzy sets,” Journal of

Geotechnical and Geoenvironmental Engineering, 2014.

Juang, C.H., *Wang, L., Hsieh, H.S., and Atamturktur, S., “Robust geotechnical

design of braced excavations in clays,” Structural Safety, Vol. 49, 2014, pp. 37-44.

*Gong, W., *Wang, L., Juang, C.H., *Zhang, J., and Huang, H., “Robust

geotechnical design of shield-driven tunnels,” Computers and Geotechnics, Vol. 56,

March 2014, pp. 191-201.

Juang, C.H., *Wang, L., *Liu, Z., Ravichandran, N., Huang, H., and Zhang, J.,

“Robust geotechnical design of drilled shafts in sand - A new design perspective,”

Journal of Geotechnical and Geoenvironmental Engineering, Vol. 139, December

2013, pp. 2007-2019.

*Wang, L., *Hwang, J.H., and Juang, C.H., and Sez Atamturktur, “Reliability-based

design of rock slopes – A new perspective on design robustness,” Engineering

Geology, Vol. 154, 2013, pp. 56-63.

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Thank You！

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Load and Resistance Factor Design Considering Design ...hsein/wp-content/uploads/2017/01/Load... · Load and Resistance Factor Design Considering Design Robustness: R-LRFD ... Load