[American Society of Civil Engineers International Deep Foundations Congress 2002 - Orlando,...

Seismic Foundation Stiffness For Bridges

Zia Zafir, Ph.D., M. ASCE

Senior Seismic Engineer, Kleinfelder, Inc., 7133 Koll Center Parkway, Suite 100, Pleasanton, CA 94566; PH 925-484-1700; FAX 925-484-5838; [email protected]

Abstract

This paper presents a simple procedure to develop stiffness matrix for bridge foundations under seismic loading conditions. The methodology is based on the results of a pilot program for the Washington State Department of Transportation in which a design manual was developed to assist the bridge engineers for seismic design of bridge foundations for typical bridges in the state. The proposed procedure consists of a simple approach, which combines the results of a dynamic soil-structure interaction finite element program SASSI (Lysmer et. al., 1981) with the results of SHAKE (Sclmabel et. al., 1972), LPILE (Ensoft, 1998a) and APILE (Ensoft, 1998b) to develop stiffness matrices of pile group/shaft foundations, which are more realistic. The results are presented in the form of design charts, which show the variation of horizontal, vertical, rocking, torsional, and cross coupling stiffness components with the deflection. The results of our analyses show that the cross coupling terms are important for single shafts but can be ignored for the pile groups. In addition, we found that the contribution of the pile caps in the lateral stiffness of pile foundation can be as high as 75 percent of the total stiffness.

Introduction

One of the important geotechnieal parameters for seismic analysis of bridge structures is the foundation stiffness. More precisely, the bridge engineer needs a set of boundary element springs, which can represent the foundation stiffness versus deflection along different axes. These foundation spring elements are then attached to the structural dynamic model of the bridge undergoing seismic analysis. A complete set of foundation springs (stiffness matrix) includes horizontal, vertical, rocking, torsional and cross coupling components.

This paper presents a simple procedure to estimate the foundation stiffness versus deflection for different levels of seismic shaking for typical bridge foundations. The main emphasis is to provide simple and routine practical procedure that can be used by bridge engineers to evaluate foundation stiffness for seismic bridge analysis. The proposed approach presents simple methods to account for (i) cross coupling stiffness terms for single shafts, (ii) interaction between piles in the group, and (iii) stiffness of pile caps.

Definition Of Foundation Stiffness

The response of the foundation substructure can be fully described by six degrees of freedom (three translations and three rotations) at the center of the pile cap (or single pile) cutoff section, as shown in Figure 1. Assuming that {P} and {A} are 6xl vectors

1421

Deep Foundations 2002

Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

1422 DEEP FOUNDATIONS 2002

containing boundary forces (or moments) and deflections (or rotations), respectively, and [K] is the 6x6 foundation stiffness matrix at the foundation eutoffpoint, we can write:

where:

and

{v} = [K]. {A} O)

{P} = <P, P2 Ps M, M 2 M,>'r (2)

{A} = <A, A~ A3 0~ 0~ 0~>T (3)

PI. P2 and P3 are the forces in local axes 1, 2 and 3, respectively,

MI. M 2 and M 3 are the moments in local axes 1, 2 and 3, respectively, Aj, A 2 and A3 are the deflections in local axes 1, 2 and 3, respectively,

01, 02 and 03 are the rotations in local axes 1, 2 and 3, respectively.

All foundation cases considered in this paper are symmetric about their local horizontal 1- and 3- axis (e.g. see Figure 1). For these foundations, the stiffness matrix is uncoupled in the horizontal and vertical directions and may be written as follows:

I Kll 0 0 0 0 -Kl6 "7 0 K22 0 0 0 0

J [K] = 0 0 K~3 K34 0 0 (4) 0 0 K43 K , 0 0 0 0 0 0 Ks5 0

-IGl 0 0 0 0 IG,

where: K~l and K33 are the horizontal stiffiaesses along axes 1 and 3, respectively (kN/m); K22 is the vertical stiffness along vertical axis 2 0oN/m); I ~ and K~ are the rocking stiffnesses about axes 1 and 3, respectively (kN-m/rad); Ks5 is the torsional stifflless about vertical axis 2 (kN-m/rad); K16=K,1 and K34=K43 are the cross coupling stiffnesses (kN/rad or kN-m/m).

The pile group foundations with rigid pile cap considered in this paper derive resistance to rocking mainly by the axial forces (compression and tension) in the piles about the corresponding axis of rotation. For these foundations, the cross coupling between horizontal and rocking stiffnesses are small and may be neglected; i.e. KI6 = Krl =

K34 = K43 = 0. Single piles/shafts, on the other hand, resist the rocking mainly by the flexural stiffness and, therefore, exhibit a strong coupling between horizontal and rocking stiffnesses. For these foundations, the cross coupling stiffnesses (KIr, K61, K34 and K43) are important and should be considered in the analysis.

Overview Of Foundation Stiffness Methods Many researchers have presented methods to develop the stiffnesses for pile foundations under seismic loading condition. An overview of these methods may be found elsewhere (Norris, 1995a; Lam et. al., 1986 and 1990; Martin and Lam, 1985). Most of the


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

DEEP FOUNDATIONS 2002 1423

researchers relied on finite element methods, which are often time consuming, to fully describe soil structure interaction between the soils and the foundation. In addition, none of these methods provide any simple way to establish stiffness matrices varying with the deflection for a bridge foundation. Some of the issues, which were not completely addressed previously include (i) the contribution of pile cap to the foundation stiffness, (ii) pile interaction in a group, and (iii) the cross coupling effects.

Bridge design engineers often utilize the passive pressure in front of the pile cap to include the lateral resistance due to pile cap. The passive pressure is then added to the pile group lateral resistance for the total lateral resistance of the foundation. Although, the lateral resistance of a pile group is associated with a certain level of pile top deflection, the additional pile cap resistance is not usually related to the same deflection level. In addition, the side shear resistance on the pile cap is often ignored, which often results in very little contribution from the pile cap when compared to the lateral resistance from the pile group. Zafir and Vanderpool (1998) showed that the pile cap stiffness could be more than 50% of the total foundation stiffness. Recently, Mokwa and Duncan (2001) have performed several field tests and showed that the pile cap provided approximately 50% of the overall stiffness of piles groups to lateral loads.

Pile interaction in a group has been addressed qualitatively in the past. Researchers have presented empirical group reduction factors based on pile spacing only. However, we have found that the group reduction factors depend on level of load, pile diameter, pile stiffness, pile head fixity, soil type and spacing between the piles 0Oeinfelder, 1997).

Cross coupling between horizontal and rocking stiffness, in general, has been ignored previously. An uncoupled approach is usually employed to develop stiffiaess matrix (Lain et. al., 1986 and 1990). However, results of our analyses show that cross coupling in single piles/shafts is quite important and can not be ignored.

This paper presents a simple approach, which can be used by the design engineers readily to develop the stiffness matrix. The procedure used in this paper to develop foundation stiffnesses under seismic loadings uses combination of several methods: Computer programs LPILE and APILE were used to develop nonlinear lateral and axial stiffnesses of single pile; equivalent linear three-dimensional finite element analyses were performed to estimate the interaction factors for pile groups; SHAKE was used to evaluate free field deflections of the foundation under seismic loading and limit equilibrium method was used to develop lateral stiffness of pile caps. In addition, a simple method is employed to develop the pile cap stiffnesses varying with deflection.

Only a brief description of the proposed method is presented below. Detailed description of the methodology used in this paper can be found elsewhere (Kleinfelder, 1997).

Overall Approach For Developing Stiffness Charts

Proposed Steps. The following steps summarize the proposed approach. 1. Perform one-dimensional site response analysis using the computer program SHAKE

and appropriate time history. 2. Estimate strain compatible soil properties from the results of site response analyses. 3. Establish average soil properties of the soil profiles. 4. Foundation Stiffness for Single Pile/Shaft


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.


�9 Compute horizontal (Kll and K33), rocking (K , and I ~ ) and coupled stiffness (K~6 = Krj and K34 = I~3 ) versus deflection of single pile using the results of computer code LPILE. Details of computing cross coupling terms will be discussed later.

�9 Compute vertical stiffness (K22) versus deflection of single pile foundation using the results of computer program APILE.

�9 Ignore torsional stiffness (I~5) of single pile foundation. 5. Foundation Stiffness for Pile Group Foundations

�9 Compute horizontal stiffness CKp.~t and Kp.33 ) versus deflection for a single pile in the group using the computer program LPILE.

�9 Compute vertical stiffness (K.p,22) versus deflection for a single pile using the computer program APILE.

�9 Calculate pile group reduction factors for horizontal and vertical group stiffnesses for each soil profile/foundation combination using the finite element soil- structure interaction method utilized in the computer program SASSI.

�9 Calculate horizontal (K H and K33 ) and vertical stiffness (1(22) of pile group using the horizontal and vertical stiffness of single pile and pile group reduction factors obtained above.

�9 Calculate rocking ( I ~ and K~) and torsional (I~s) stiffnesses of pile group using the vertical and horizontal stiffness of single piles, respectively.

�9 Calculate the stiffness of pile cap using limit equilibrium method. A brief summary of this method will be presented later.

�9 Combine lateral pile group and cap stiffnesses to obtain the total foundation stiffness versus deflection. It should be noted that the stiffness values for pile group and pile cap should be added at the same deflection levels. There is no cap contribution to vertical and rotational stiffnesses.

6. Estimate the foundation deflection, Ao, corresponding to the free field shear strain levels generated by seismic shaking from Item 1.

7. Truncate the maximum value of stiffness of each spring at its corresponding at free field deflection level, A o (Norris, 1995b). The saane value of vertical deflection is used for both vertical and rotational springs.

Single Pile Stiffness. In calculating the lateral pile stiffness, it is important that the cumulative effect of soil strains caused by combined shear and moment applied simultaneously at pile top be accounted for (Norris, 1986). This can be simply expressed as follows:

~prn > ~p + ~m ~ Apm ~> Ap h- m m t~ 0pm > 0p q- 0 m (5)

where: ~-~--pm = strain in soil due to combined effect of lateral load and moment at pile top

= strain in soil due to lateral load only at pile top e__ m = strain in soil due to moment only at pile top ~pm = pile top deflection due to combined effect of lateral load and moment at pile top Ap = pile top deflection due to lateral load only at pile top


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.


Am = pile top deflection due to moment only at pile top 0m = pile top rotation due to combined effect of lateral load and moment at pile top 0p = pile top rotation due to lateral load only at pile top 0 m = pile top rotation due to moment only at pile top

The following procedure should be followed to properly account for the effect of increased soil strains in calculating single pile stiffness due to coupled lateral force and moment acting at the pile top: 1. Apply the lateral force (P) and moment (M) simultaneously to the pile top and calculate

the resulting soil strains ( . ~ and pile head deflections (~m and 0v,0. 2. Using soil strains ~ established above with no more iterations on soil properties,

analyze pile response due to the lateral force (P) and moment 0VI) applied separately at the pile top. This analysis will result in:

Apm = Ap + Am & 0pro = 0 v + 6 , (6)

3.

It is noted that (Ap and 0p) and (Am and 0~) obtained above are different from and, in general, larger than those obtained from applying lateral force and moment separately and iterating on soil properties. Form the flexibility matrix:

F = I (7) 10./P I

4. Calculate pile head stiffness from:

1 0 m ~ - A m ~ I K = F-' = I �9 v . M / ( N . 0 ~ am)

I-0p/P Ap/P I (8)

5. Repeat steps (1) through (4) for different pairs of shear force and moment.

However, the above procedure turns out to be difficult to apply using LPILE code. LPILE currently do not allow lateral analyses of piles to be performed without iterating on soil P-Y curves. Because manual manipulation to incorporate this procedure becomes very tedious and time consuming, we have developed a simplified procedure to develop coupled foundation stiffnesses due to combined lateral force and moment applied at the pile top. Steps 1 and 2 presented above should be replaced by the following four steps. 1. Apply the lateral force (P) and moment (M) simultaneously to the pile top and calculate

the resulting soil strains (~--pm) and pile head deflections (Apm and 0pm ). 2. Reduce the ultimate soil shear resistance, say by 20%, and perform lateral analyses of

the pile with both lateral force and moment applied independently at the pile top. This will result in (Ap and 0p) and (A m and 0,1) which, in general, are larger than those


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.


3.

obtained from applying lateral force and moment separately and iterating on soil properties. Compute the deflections and rotations at the pile top from Step (I) and (2) to cheek whether:

Am= Av+Am & 0pro = 0~+0m (9)

4. If equality in the above equations does not hold with some acceptable tolerance, go back to Step (2) and adjust the ultimate soil shear resistance accordingly and repeat the analyses until the above equation is satisfied.

Repeat Steps 3 through 5 from the first procedure and use equations (7) and (8) to form flexibility and stiffness matrices.

Lateral Stiffness of Pile Caps. Details about the method to estimate the lateral stiffness of pile caps can be found in Kleinfelder (1997). A summary of our proposed method to estimate contribution of pile cap to lateral stiffness of the foundations are presented below: (i) Estimate the ultimate passive soil resistance (Fp) by assuming a passive wedge type

failure. (ii) Estimate the maximum deflection (Amax) necessary to develop ultimate passive

resistance. Based on the behavior of retaining structures, the maximum deflection A m a x varies from .002H to .04H depending on the soil type and condition (NAVFAC Design Manual 7.02, 1982). This will determine the maximum point on a load versus deflection curve.

(iii) Evaluate the initial slope of load-deflection curve (kmax) using the procedure

presented by Gazetas (1991) in which the static stiffness of a foundation embedded in a homogenous halfspace can be calculated. For the pile group ease, the resistance between the bottom of the pile cap and the soil should not be considered. This can be achieved by subtracting the stiffness of a surface foundation from that of an embedded foundation.

(iv) Construct the load versus deflection curve using modified hyperbola:

where: P

Rf

P = A / (1/kma x + Rfx A / Fp) (10)

Load at deflection A, Fp = Ultimate passive force, kma x = Initial stiffness Ratio between the actual and the theoretical ultimate force. It can be determined

by substituting Ama x for A and Fp for P in the above equation.

Group Effects from Soil Structure Interaction Analysis. We have followed the general procedure outlined by Poulos (1979) to estimate the group reduction factors. Soil structure interaction (SSI) analyses were performed using the computer code SASSI (Lysmer et. al., 1981) to evaluate the pile group interaction factors.

In SASSI analysis, concrete piles were modeled as one-dimensional beam elements embedded in a semi-infinite horizontally layered soil system. Strain compatible free field


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.


soil properties were obtained from the SHAKE analysis of soil profiles SP1 and SP2 for an appropriate time history.

Figure 2 presents the results of the SASS1 analyses in terms of s/d ratio (ratio between the pile spacing and pile diameter) versus pile interaction factor (et) for soil profiles SP1 and SP2 shown in Figure 3. Pile interaction factor is defined as the ratio of the deflection of the reference pile in a two pile group (D2) to the deflection of the single

reference pile (D1) minus 1:

= D2/D 1 - 1 (11)

Pile interaction factors for vertically and laterally loaded piles (where the load is parallel and perpendicular to the centerline of the piles) can be directly obtained from Figure 2. As can be seen from the above figure, piles loaded parallel to their centerline show larger interaction as compared to the transversely loaded piles.

For laterally loaded piles where the load has a general orientation with respect to the centerline of the piles, the interaction factor is obtained by interpolation given below:

% = e t , + ( c q - c Q . 0 / 9 0 ~ (12)

where or, and oq are the lateral interaction factors for piles loaded parallel and perpendicular to the centedine of piles, respectively, and 0 is the angle (in degrees) of the load with respect to centerline of piles. The pile group reduction factor 13 can be calculated by

13j = 1/(1+ (Z%.O) ; i--- 1, 2 ..... n-1 ; j = 1, 2, 3 (13) w h e r e i

%, i = Interaction factor for Pile i in the group along j-axis 13i = Group reduction factor, 0 < 13j < 1

eq, i should be calculated for each pile in the group using the charts presented in Figure 2.

Pile Group Stiffness, K a.

Horizontal and Vertical Stiffness. group, K~, were calculated from the following equation:

K~ji=Kpjj.n.13i ; j = 1 , 2 , 3 where:

K~ :- Translational stiffness of pile group along j-axis Kp~ = Translational stiffness of single pile along j-axis n = Number of piles in the group [3j = Group reduction factor, 0 < [3j _< 1

Horizontal and vertical stiffness of the pile

(14)

Rocking and Torsional Stiffness. The rocking (or torsional) stiffness of the pile group KGi j is calculated by adding up the vertical (or horizontal) stiffness of individual piles in the group times square of the moment arm about the corresponding axis of rotation, as defined below:


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.


where:

I ~ = E K ~ . i ' r i 2 . 1 3 i i = 1 , 2 ..... n ; j = 4 , 5 , 6 (15)

K~i i = Rotational stiffness of pile group along j-axis

Ke, i = Translational stiffness of single pile i in the group ri = Moment arm of Pile i about corresponding axis of rotation n = Number of piles in the group 13j = Group reduction factor, 0 < 13j < 1

This pile group stiffness was added to the pile cap stiffness to obtain the horizontal stiffness.

Example Problems

Six different pile/shaft foundation types and seven different soil profiles were analyzed for the State o f Washington. Details of those studies are presented in Kleinfelder (1997). Two soil profile types and three foundations types are considered in this paper. The soil profile types are presented in Figure 3 and foundation types are presented in Figure 4. Pertinent soil parameters for each soil profile are also presented in Figure 3. A brief description of soil profiles and foundation types are also presented in Tables I and 2.

Table 1: Selected Soil Proffies

Soil Profile SP1

SP2

Brief Description 9 m of very soft organic silt overlying dense to very dense silty ~'avelly sand (groundwater table at surface). 9 m of medium stiffto very stiff alluvial fi l l /day overlying dense to very dense glacial deposit (groundwater table at 1.5 m).

Table 2: Selected Foundation Types

Foundation Type PF1

PF2

PF3

Brief Description Single cast-in-place concrete pile foundation with 1800-ram diameter. The upper 9 m of pile in soil profile SP1 is cased with 19mm thick steel easing. Pile group of four 1220-mm diameter piles with 6 m x 6 m x 2 m embedded pile cap. The upper 9m of pile in soil profile SP1 is cased with 12.7mm thick steel casing. Pile group of nine 610-mm diameter piles with 5.8 m x 5.8 m x 2 m embedded pile cap. The pile consists of 12.7 mm thick steel pipe pile filled with concrete.

For the purpose of estimating foundation stiffnesses, the pile lengths were assumed to be on the order of 24-30 m 'in soil profile SP1; 12-18 m in soil profile SP2 for foundation types PF1 and PF2; 18-24 m in soil profile SP2 for foundation type PF3. Table 3 provides pertinent soil properties for soil profiles SP1 and SP2 used in computer program LPILE.


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.


Depth (m)

0-9 9-60

0-9 9-60

Table 3: Soil Properties for Input in LPILE

(kN/m 3) (MN/m 3) ) (kN/m 2)

Soil Profile SPI 12.6 [ 7.6 I - I 9.6 [ .030 2 1 . 2 1 34 [ 40 ] ]

Soil Profile SP2 18.1 I 136 I I 72 I .007 2 1 . 2 1 34 I 40 [ - I

Results And Discussions

The analyses involved several steps including: (i) estimating free field deflections under seismic conditions to limit the maximum value of stiffnesses; (ii) calculating group reduction factors for the pile groups; (iii) estimating initial foundation stiffnesses by combining the response of piles and pile caps; and (iv) developing normalized stiffness values versus deflection to be used in the design. The stiffness matrix at a certain deflection level is developed by multiplying the normalized value (read from the chart for that deflection level) with the maximum value (listed in the table). All of the above mentioned steps are discussed briefly over here.

Results

Free Field Deflections. The results of the SHAKE analyses in terms of free field deflections for the two soil profiles and three foundation types are presented in Table 4. It is assumed that under the seismic loading conditions, the maximum (initial) stiffness should be limited to the value associated with these free field deflections. Lateral and vertical displacements are taken to be the same.

Table 4: Free Field Deflections, A o

Soil Profile SP1 SP2

Foundation Type PF 1 PF2 PF3 PF 1 PF2 PF3 Ao mm (in) 19 (.75) 1.3 (.05) 1.3 (.05) 3.8 (.15) 1.3 (.05) 1.3 (.05)

Group Reduction Factors. Results of the SASSI analyses to estimate pile interaction factors for foundation types PF2 and PF3 are presented on Figure 4. Using equations (11), (12), and (13), the group reduction factor 13 for each foundation and soil profile type was estimated. These values of [3 are listed in Table 5.


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

1430 D E E P F O U N D A T I O N S 2002

Table 5: Group Reduction Factors

Soil Profile Foundation 131 [3 2 [3~ Type Type Free Fixed Free Fixed Free Fixed SP1 PF2 0.55 0.60 0.83 0.83 0.55 0.60

PF3 0.35 0.40 0.68 0.68 0.35 0.40 SP2 PF2 0.67 0.60 0.73 0.73 0.67 0.60

PF3 0.48 0.41 0.56 0.56 0.48 0.41

Note that vertical (and, therefore, rotational) stiffnesses as given by 132 is independent of pile head fixity.

Maximum (Initial) Foundation Stiffnesses, K,. The initial foundation stiffness values (Ko.tl, K 0.2, K 0.33, K 0,44, K o.ss, Ko.66, K 0.16 = K 0.6, and Ko,34 : K 0,43) for the soil profile/foundation combination under consideration were obtained using equations (7), (8), and (9) for foundation type PF1 and, in addition, equations (10), (14), and (15) for foundation types PF2 and PF3, which include the pile cap stiffness. Table 6 provides stiffness values for both fixed and free pile head conditions. For single pile foundation type PF1, the actual moment/rotation condition at the pile cutoffpoint was considered.

Table 6: Initial Foundation Stiffnesses

Soil Foundation Pile/Pile Cal I ~ , K,a 2 I~33 K~. K~55 K.~ K,a,-(=K,.611 ~4(=K0.43' Profile Type Connection (kN/m) 0dq/m) (kN/m) (kN-mh'ad) (kN-m/rad) (kN-m/rad) (kN/rad) (kN/rad)

P F I 1.94E+05 2.89E+06 1.94E+05 6.58E+06 6.58E+06 9.07E+05 9.07E+05 PF2 Fixed 3.54E+05 4.31E+06 3.54E+05 3.12E+07 1.58E+06 3.12E+07

S P I Free 2.00E+05 4.31E+06 2.00E+05 3.12E+07 5.53E+05 3.12E+07

PF3 Fixed 2.38E+05 4.20E+06 2.38E+05 9.38E+06 5.44E+05 9.38E+06

Free 1.58E+05 4.20E+06 1.58E+05 9.38E+06 1.84E+05 9.38E+06

PF1 2.49E+06 4.59E+06 2.49E+06 1.20E+07 1.20E+07 5.16E+05 5.16E+05 PF2 Fixed 1.67E+06 5.99E+06 1.67E+06 2.00E+07 7.14E+06 2.00E+07

SP2 Free 1.04E+O6 5.99E+06 1.04E+06 2.00E+07 2.97E+06 2.00E+07

PF3 Fixed 1.61E+06 4.62E+06 1.61E-tO6 1.03E+07 4.57E+06 1.03E+07

Free 1.39E+06 4.62E+06 1.39E+06 1.03E+O7 3.57E+06 1.03E+07

(1) vertical stiffness, Ko,22 , or rotational stiffnesses Ko,44 and Ko.66 are independent of pile head fixity. (2) Cross coupling terms Ko,16 and Ko,34 are in kN/rad while Ko.61 and Ko.43 are in kN-m/m.

Normalized Stiffness Charts. Stiffness versus deflection values were normalized against the initial stiffness values. The normalized stiffness charts are presented in Figure 5 for foundation type PF1 and in Figures 6 and 7 for foundation types PF2 and PF3, respectively. For a given deflection and/or rotation value, the normalized stiffness is read from the charts presented on Figures 5 through 7. Then the normalized stiffness value is multiplied by the initial stiffness given in Table 6 to obtain the actual stiffness associated with the given deflection and/or rotation. It should be noted that the normalized stiffnesses presented in Figures 5 through 7 should be truncated at free field deflection value Ao, which are presented in Table 4 for different foundation and soil types.

Pile Cap Contribution. We have also calculated the contribution of pile cap to the total stiffness of a foundation system. Figure 8 shows the pile cap contributions for both


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.


foundation types PF2 and PF3 for soil profile types SP1 and SP2. It can be seen that the contribution of pile cap depends on the size of the pile cap, pile head fixity, and the soil profile type.

Discussion

Based on the results of the analyses presented above, the following observations are made. �9 Free field deflections under seismic loading conditions depend on the type of soils and

thickness of the pile cap. �9 It can be seen from Table 5 that the group reduction factor depends not only upon pile

spacing, but on type of foundation, soil profile type, and pile group configuration as well.

�9 The normalized stiffness charts show that the variation in stiffness with deflection is quite significant. It takes less than 5 mm of deflection to reduce the lateral stiffness by more than 50%. However, the vertical and rocking stiffiaesses of a pile group are less sensitive to deflection and rotation, respectively.

�9 Stiffness of a pile cap is quite significant in the lateral direction and can be as high as 75% of the total foundation stiffness in that direction.

�9 In general, the cap contribution is greater for the free versus the fixed head pile to pile cap connection.

�9 The contribution of the pile cap stiffness increases with deflection initially and then it decreases with deflection. This is due to the fact that a certain amount of movement is needed to mobilize passive pressure.

�9 Torsional stiffness can be ignored for the single pile but is quite important for the pile group. On the other hand, cross coupling stiffness can be ignored for the pile group but is very important for the single pile.

Conclusions

1. Although the response of bridge foundations under seismic loading conditions is a complex phenomenon, it can be simplified by using the proposed procedure to develop foundation stiffness versus deflection, which utilizes existing analysis tools available to the design engineer.

2. It has been shown that interaction between piles in a group is an important factor to consider. A more elaborate finite element based method is utilized in this paper to calculate the group reduction factor, which may not be easily available to the design engineers. However, any empirical reduction factor can be readily used in the proposed procedure to calculate the stiffness matrix.

3. It has been shown that cross coupling terms are important for the single pile foundation. A simple method for calculating the cross coupling terms is given.

4. It has been shown that the contribution of the pile cap stiffness is quite significant. A simple step by step procedure is presented to develop pile cap stiffness versus deflection.

5. By utilizing strain compatible soil properties resulting from SHAKE and limiting maximum stiffness value to the value associated with free field deflection, the seismic response of the subsurface soils can be included in a simple but realistic way.


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.


Acknowledgements

Funding to develop the design manual was provided by Washington State Department of Transportation (WSDOT). Mr. Mynt Lwin of WSDOT coordinated the overall project. Dr. J. P. Singh (formerly of Kleinfelder) of J. P. Singh & Associates directed the overall study and Dr. Mansour Tabatabaie (formerly of Kleinfelder) of MTR Associates was the project manager.

APPENDIX I. REFERENCES

Ensofi, Inc. (1998a). "LPILE Plus Version 3.0 - A Program for Analyzing Stress and Deformation of a Pile or Drilled Shaft Under Lateral Loads."

Ensoft, Inc. (1998b). "APILE Plus Version 3.0 - A Program for the Analysis of Axial Capacity of Driven Piles."

Gazetas, G. (1991). "Foundation Vibrations." Foundation Engineering Handbook, 2nd Edition, H.Y. Fang, ed, Van Nostrand Reinhold, 553-593.

Kleinfelder, Inc. (1997). "Design Manual for Foundation Stiffnesses Under Seismic Loadings." Prepared for Washington State Department of Transportation.

Lain, I. P. and Martin, G. R. (1986). "Seismic Design of Highway Bridge Foundations." FHWA Report Nos. FHWA/RD-861, FHWA/RD-86/102, and FHWA/RD-86/103.

Lam, I. P., Martin, G. R., and Imbsen, R. (1990). "Modeling Bridge Foundations for Seismic Design and Retrofitting." Transportation Research Record 1290, TRB, 113-126.

Lysmer, J., Tabatabaie, M., Tajirian, F., Vahdani, S., and Ostadan, F. (1981). "SASSI - A System for Analysis of Soil-Structure Interaction." Report No. UCB/GT/81-02, Geotechnical Engineering, University of California, Berkeley, California, April.

Martin, G. R. and Lam, I. P. (1985). "Seismic Design Procedures for Bridge Foundations." Proc., Second Joint U.S.-New Zealand Workshop on Seismic Resistance of Highway Bridges, Applied Technology Council, ATC-12-1,129-146.

Mokwa, R. L. and Duncan, J. M. (2001). "Experimental Evaluation of Lateral-Load Resistance of Pile Caps." Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 127(2), 185-192.

Norris, G. M. (1995a). "Seismic Bridge Pile Foundation Behavior." Proc., International Conference on Design and Construction of Deep Foundations, U.S. Federal Highway Administration (FHWA).

Norris, G. M. (1995b). "Pile Foundation Stiffness as a Function of Free-Field or Near-Field Soil Strain." Geotechnical Special Publication No. 51, ASCE, 32-44.


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.


Norris, G. M. (1986). "Theoretically Based BEF Laterally Loaded Pile Analysis." Proc., Third International Conference on Numerical Methods in Offshore Piling, Nantes, 361- 386.

Poulos, H. G. (1979). "Group Factors for Pile-Deflection Estimation." Journal of the Geotechnical Engineering Division, ASCE, 105(GT12), 1489-1509.

Schnabel, P.B., Lysmer, J., and Seed, H.B. (1972). "SHAKE - A Computer Program for Earthquake Response Analysis of Horizontal Layered Sites." University of California, Berkeley, EERC - Report 72-12.

U.S. Navy. (1982). NAVFAC. "Design Manual: Foundations and Earth Structures," NAVFAC DM 7.2, Dept. of Navy.

Zafir, Z. and Vanderpool, W. E. (1998). "Lateral Response of Large Diameter Drilled Shafts: 1-15/US 95 Load Test Program." Proc., 33 "a Engineering Geology and Geotechnical Engineering Symposium, University of Nevada, Reno, NV, 161-176.


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.


Figure 1: Definition of Foundation Stiffness

Figure 2: Pile Interaction Factors, et, for Soil Profiles SP1 and SP2


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.


Figure 3: Soil Profile Types (a) SP1 and (b) SP2

Figure 4: Foundation Types (a) PF1, (b) PF2, and (c) PF3


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

1 4 3 6 D E E P F O U N D A T I O N S 2 0 0 2

1,0

O.IP,

~ 0.6

0.4

~ 0 . 2

Z~O.O

~ 1.0

~ 0.8

~ 0.6-

~ 0.4-

0 . 2

0 . 0 0.000

C.-8- SP 1 -* -SP2[

Foundation Type PFI

M ~ r~

20 40 60 Pile Head Horizontal Deflection (ram)

80

I§ -.-sP2] Foundation Type PFI

1.0

~ 0.6

.~0 .4

o~0.2 Z

0.0

1t i.o

~ 0.8

~ 0.6

~ 0.2

~ 0 . 0

[-m-sP1-1- sP2J

20 40 60

Pile Head Vertical Deflection (mm)

'-B- SP I " e - SP2 ]

Foundation Type PF 1

El R z

0.005 0.010 0.015 0.020 20 40 60

Pile Head Rotation (tad) Horizontal Deflection (mm)

Figure 5: Normalized Stiffness for Foundation Type PF1

1.0

0.8

0.6

~ 0.4 -

~ 0.2 �9

~0.C

-.41~ SP 1 - Free Head " * - SP 1 - Fixed Hea~ [-.,s- SP2 - Free Head "-',~- SP2 - Fixed He.at

ation Type PF2

, .o

g 0 . 8

0.6

~ 0.4

0.2

~ 0.2

Z 0.~

20 40 60 20 40 60

Pile Head Horizontal Deflection (ram) Pile Head Ve~ical Deflection (ram)

" . . . . ~ p e P F 2

1.0

08

~ 0.6

~ 0+4

~ 02 o Z

00

[ - '~SPI Free Head ~ S P I - Fixed Head

~ S P 2 - F r e e H e a d "-~-SP2 FxedHead

Type PF2

Z 000 0o1 002 003 004 005 000 001 002 003 004 Pile llead Rotation (rad} Pile Itead Rotation (rad)

Figure 6: Normalized Stiffness tor Foundation Type PF2

005


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.


1.01

~0 .8 -

~ 0.6-

~0 .4 - ! N0.2- g Z 0,~

-t~-SPI - Free Head --~'SPI - Fixed H ~ I I I [.-~-SP2-FreeHead .--~SP2-PixedHead

1.0

~0,$

~0.6

.~0A

~ 0.2

0,0

~0.8 .

~0.6-

~0.4-

i 0.2

0.C

m _

~ 14-sPt ~SP21

20 40 60 80 20 40 60 80 Pile Head Horizontal Deflection (ram) Pile Head Vertical Deflection (ram)

l-'m- SP I --*- sP21 ,~, I "0 T ["!'- SP 1 - Free Head "-r SPI - Fixed Head

~0.8 I ~ "~- SP2 - F i x ~ Head

~ 0 . 6 [ Foundation Type PF3

0.0 I

0.00 0.01 0.02 0.03 0.04 0.05 0.00 0.01 0.02 0.03 0.04 0.05 Pile Head Rotation (tad) Pile Head Rotation (tad)

Figure 7: Normalized Stiffness for Foundation Type PF3

t [ �9 I-~'SPI-Fret:Head -~'-SPI-FixedHead] ~z 0.81 [ ~ SP2 - Free Head --x- SP2 - Fixed Head I

�9 "s ~

~ 0.4

~ 02

0

I

.~ 08

"9 0.6

~x,~ 4

6202 -

0 -

Foundation Type PF3

~ SPI - Free Head --o-SPI - Fixed Head SP2 - Free ltead --x- SP2 - F xed Head

0 20 40 60 80 20 40 60 Pile Head Deflection (mm) Pile Head Deflection (ram)

(a) Cb)

Figure 8: Pile Cap Contribution for Foundation Types (a) PF2 and (2) PF3


Dow

nloa

ded

from

asc

elib

rary

.org

by

WA

SHIN

GT

ON

UN

IV I

N S

T L

OU

IS o

n 09

/24/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

Date post:	11-Dec-2016
Category:	Documents
Upload:	zia
View:	215 times
Download:	2 times

[American Society of Civil Engineers International Deep Foundations Congress 2002 - Orlando,...

Documents