numerical methods for pile modeling

Mohammad Reza Falamarz-SheikhabadiCandidacy Exam

Fall 2012

Critical Review of Analytical and Numerical Modeling of Pile Foundations Subjected to

Earthquake Loading

1Drexel University, Civil Engineering Department

Pile foundation definition Different methods for pile modeling

Winkler method Beam on nonlinear Winkler foundation (BNWF) Finite element method

Absorbing boundary conditions Viscous damping boundary model Perfectly matched layer

Discussion on BNWF Conclusion References

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Contents

Drexel University, Civil Engineering Department

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Pile Foundation Definition

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Pile Foundations

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Pile usually represents a slender structural element that is driven into the ground. However, a pile is often used as a generic term to represent all types of deep foundations.

Here, I talk about normal size piles (250-600 mm)

Ref. 1

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Pile Foundations

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Different types of pile foundations to carry vertical, horizontal or inclined loads from superstructure.

Ref. 2

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Individual Pile and Pile Group

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Pile foundations may consists of an individual pile or a group of piles. Although a pile group is composed of a number of individual piles, the behavior of a pile group is not equivalent to the sum of all the piles as if they were separate individual piles

Ref. 2

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Individual Pile and Pile Group

Drexel University, Civil Engineering Department

The behavior of a pile group is more complex than an individual pile because of the effect of the combination of piles, interactions between the piles in the group, and the effect of the pile cap.

Ref. 2

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Pile Modeling Methods

Drexel University, Civil Engineering Department

Continuum method Winkler method Beam on nonlinear Winkler foundation Finite element method

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Pile Modeling

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Ref. 3

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Winkler method

Drexel University, Civil Engineering Department

The Winkler approach is the oldest method for estimating pile deflections and bending moments. The approach model the soil as a series of unconnected linear springs with stiffness, Es, expressed in units of force per length.

Ref. 2

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Winkler method

Drexel University, Civil Engineering Department

Limitations:

1. The method ignores the nonlinear characteristics of soil.

2. The axial load effects are ignored.

3. The soil model used in the technique is discontinuous.

Ref. 2

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Beam on nonlinear Winkler foundation (BNWF)

Drexel University, Civil Engineering Department

The p–y method is versatile and can be used to solve problems including different soil types, layered soils, nonlinear soil behavior, different pile materials, cross sections, and different pile head connection conditions.

Confining pressureRef. 4

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Beam on nonlinear Winkler foundation

Drexel University, Civil Engineering Department

Considering that both piles and soil can behave in a nonlinear manner during extreme events, the use of p-y methods for defining the lateral stiffness of pile-soil model for seismic analysis (secant stiffness as a function of pile deformation) has been used since the seventies.

Why sometimes I have used p-y elements and sometimes p-y springs?

Ref. 5

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Beam on nonlinear Winkler foundation

Drexel University, Civil Engineering Department

Ref. 1

In this method, the reaction of soil surrounding the pile is modeled as localized springs: a series of springs along the shaft (the t-z curves) and the spring attached to the tip or bottom of a pile (the Q-z curve). The load transfer or unit friction force along the shaft is shown by t, Q is the tip resistance of the pile in compression, and z is the settlement (for static analysis) or vertical deformation (for dynamic analysis) of soil at the location of a spring.

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BNWF and Pile group

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Since analyzing the pile group supported structures under lateral loading needs including the effects of rocking motions, in the BNWF, all localized nonlinear springs, namely, p-y, t-z and Q-z should be considered Ref. 6

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BNWF and Pile group

Drexel University, Civil Engineering Department

Side-by-side

spacing

Corner pile moment

modification factor

3D 1

2D 1.2

1D 1.6

The bending moments for the corner piles should be increased for closely spaced piles

Ref. 2Ref. 8

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P-multiplier

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A popular method to account for shadowing effect is to incorporate p-multipliers into the p-y method of analysis. The p-multiplier values depend on pile position within the group and pile spacing.

Ref. 7

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P-multiplier

Drexel University, Civil Engineering Department

Factors influencing p-multiplier: pile spacing group arrangement group size pile head fixity soil type and density

Ref. 8

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Beam on nonlinear Winkler foundation

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Limitations:

1. The p-y method is based on pseudo-static loading for while lateral forces from the upper structure are only applied,

2. The accuracy of the p–y method depends on the number of tests and the variety of tested parameters, such as geometry and stiffness of pile, layers of soil, strength and stiffness of soil, and loading conditions.

3. The effects of pile diameter have not been considered in the primary relations of p-y curves.

4. The pile cap effects are usually ignored and cap pile are considered rigid.

5. For pile groups, using p-multiplier method oversimplifies the problem.

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Finite element method

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The FE method has the ability of permitting to account for soil nonlinearity by applying appropriate constitutive models, such as the Drucker-Prager, Cam-Clay or Mohr Coulomb formulation, and to use gap-elements to model possible pile soil separation.

Too difficult and time consuming!

Ref. 9

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Finite element method

Drexel University, Civil Engineering Department

Limitations:

1. The cost of the specialized software.2. The time consuming model

generation.3. The time required for the non-linear

analysis.4. The difficulty in the interpretation of

the result in terms of common pile (beam) variables.

5. The uncertainties associated with soil non-linear modeling in 3D.

Ref. 9

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Absorbing Boundary Conditions

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Absorbing boundary conditions

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Semi-infinite medium

Bounded medium

Bounded medium

The boundaries absorb the waves should be transmitted in semi-infinite medium.

Viscous damping boundary method Perfectly matched layer Infinite elements Consistent dashpot, spring and mass method And other numerical methods

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Absorbing boundary conditions

Drexel University, Civil Engineering Department

Ref. 3

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Viscous damping boundary method

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The simplest local ABC is the classical normal impedance or standard viscous boundary. Its performance is known to deteriorate as the position approaches the source of perturbation especially in the low-frequency limit.

This method has been modified in different manners!Ref. 10

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Viscous damping boundary method

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1. It can be only used for dynamic analyses.

2. The method is able to absorb only primary and secondary waves under an angle of incidence of 90o.

3. The interested medium should be elastic and linear.

Ref. 10

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Perfectly matched layer

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The PML is only reflectionless when the exact wave equation is solved. In practical applications, when the approximate methods like finite-difference-time-domain (FDTD) or FE are applied for modeling, the analytical perfection of the PML is no longer valid and so user should consider this point in the analysis.

!!!Soil=Elastic Medium!!!

Ref. 12

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Perfectly matched layer

Drexel University, Civil Engineering Department

A newly discovered silent boundary is the perfectly matched layer method, first introduced for the use of electromagnetic waves. The concept has been designed designed to absorb thoroughly any incident wave without reflection, for any incident angle and at any frequency before discretization.

Ref. 11

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Perfectly matched layer

Drexel University, Civil Engineering Department

Ref. 11

1. When the approximate methods like finite-difference-time-domain (FDTD) or FE are applied for modeling, the analytical perfection of the PML is no longer valid and so user should consider this point in the analysis.

2. Interested region should be elastic (such an assumption for soft or saturated soil condition and large-scale structures is absolutely unacceptable).

3. Its performance depends on the type of seismic waves.

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Discussion on BNWF

Drexel University, Civil Engineering Department

In spite of the fact that the seismic responses of structures are resultant of the combined action of at least three translational components of ground motion (ignoring two rocking and one torsional earthquake components), the coupling effects of these components in the modeling of pile foundations are commonly ignored in the analytical and numerical studies.

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Discussion

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Earthquake Components

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0 20 40 60 80 100-50

-40

-30

-20

-10

0

10

20

30

40

t

a R(t

) c

m/s

/s

0 20 40 60 80 100-40

-30

-20

-10

0

10

20

30

40

50

ta T

(t)

cm

/s/s

0 20 40 60 80 100-20

-15

-10

-5

0

5

10

15

20

t

a V(t

) c

m/s

/s

0 20 40 60 80 100-15

-10

-5

0

5

10

15

t

a R

(t)

mra

d/s

/s

0 20 40 60 80 100-10

-5

0

5

10

15

t

a T

(t)

mra

d/s

/s

0 20 40 60 80 100-25

-20

-15

-10

-5

0

5

10

15

20

t

a V

(t)

mra

d/s

/s

Translational components

Rotational components

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Earthquake Components

Drexel University, Civil Engineering Department

Translational components

Rotational components

0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000

8000

(Hz)

AR

()

0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000

8000

(Hz)

AT

()

0 5 10 15 20 25 30 350

500

1000

1500

2000

2500

3000

3500

4000

4500

(Hz)

AV(

)

0 5 10 15 20 25 30 350

500

1000

1500

2000

2500

(Hz)

A

R(

)

0 5 10 15 20 25 30 350

200

400

600

800

1000

1200

1400

1600

1800

(Hz)

A T

()

0 5 10 15 20 25 30 350

500

1000

1500

2000

2500

3000

3500

4000

(Hz)

A V

()

Pile caps are often considered rigid and their effects in lateral resistance of pile group are considered ignorable. Both of these assumptions may cause an unknown error in estimation of actual behavior of pile foundations.

Based on the size and configuration of pile group, spatial variation of strong ground motions, uncertainty in distribution of mass and stiffness of piles, unequal distribution stress on piles (shadowing effects), probable damages and torsional earthquake component; a considerable torsional moment may induce in the pile caps. This effect is usually ignored in the typical two-dimensional analyses.

Although there are many recorded data on the ground surface due to various earthquakes in different site conditions, it is not the case for data recorded underground surface. Therefore, more data are required to estimate the seismic loading of deep piles. It should be pointed out that soil is more anisotropic and non-homogenous in depth.

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Discussion

Drexel University, Civil Engineering Department

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Conclusion

Drexel University, Civil Engineering Department

Based on the previous research on soil-pile interaction, although it seems that the p-y method can be considered as an efficient technique applicable to many practical applications, it still needs some modifications and developments in order to give more reliable results in the soil-pile interaction analyses.

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Conclusion

Drexel University, Civil Engineering Department

1. Chen, W. F, Duan, L, Bridge Engineering Handbook, CRC press LLC (2000).

2. Murthy, V. N. S, Geotechnical Engineering: Principles and practices of soil mechanics and foundation engineering, Marcel Dekker, Inc.

3. Shin, H, Arduino, P, Kramer, S. L, Mackie, K, Seismic response of a typical highway bridge in liquefiable soil.

4. Gazetas, G, Dobry, R, Simple Radiation Damping Model for Piles and Footings, Journal of Engineering Mechanics ASCE, Vol. 110 (1984) 937-956.

5. Boulanger, R. W, Curras, C. J, Kutter, B. L, Wilson, D. W, Abghari, A, Seismic soil-pile-structure interaction experiments and analyses, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 125 (1999) 750-759.

6. Curras, C. J, Boulanger, R. W, Kutter , B. L, Wilson, D. W, Dynamic experimental and analysis of a pile-group-supported structure, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 127 (2001) 585-596.

7. Comodromos, E. M, Papadopoulou, M. C, Explicit extension of the p-y method to pile groups in cohesive soils, Computers and Geotechnics, Vol. 47 (2013) 28-41.

8. Mokwa, R. L, Investigation of the resistance of pile cap to lateral loading, PhD thesis, Virginia Polytechnic Institute and State University (1999).

9. Yang, Z, Jeremic, B, Numerical analysis of pile behavior under lateral loads in layered elastic-plastic soils, International Journal for Numerical Methods in Geomechanics, Vol. 2 (2002) 1-31.

10. Kramer, Steven L, Geotechnical earthquake engineering, Prentice Hall, Inc., Upper Saddle River, New Jersey, (1996).

11. Basu, U, Chopra, A. K, Perfectly matched layers for time-harmonics elastodynamics of unbounded domains: theory and finite-element implementation, Computer methods in applied mechanics and engineering, 192 (2003) 1337-1375.

12. Hasting, F. D, Schneider, J. B, Broschat, S. L, Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation, Journal of Acoustic Society of America, 100 (1996) 3061-3069.

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References

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Thank you