JP Singh and Associates in association with Mohamed Ashour, Ph.D., P.E. Gary Norris, Ph.D., P.E. March 2004 COMPUTER PROGRAM S-SHAFT FOR LATERALLY LOADED

JP Singh and Associates

in association with

Mohamed Ashour, Ph.D., P.E.Gary Norris, Ph.D., P.E.

March 2004

COMPUTER PROGRAM S-SHAFT FORLATERALLY LOADED LARGE DIAMETER

SHORT SHAFTS IN LAYERD SOIL

Workshop Objectives

• Why should we use the S-SHAFT program? • Concepts employed in the S-Shaft program• Implementation of the S-Shaft with bridge

foundations• Capabilities of the S-Shaft program• Program validation and WSDOT example

problems• Program demonstration• Future work in the next phase

y

p(Es)1

P o

(Es)3

(Es)4

(Es)2p

p

p

y

y

y

(Es)5

p

y

Laterally Loaded Pile as a Beam on Elastic Foundation (BEF)

P P

K1 K2

4 ft4 ft

Effect of Structure Cross-Sectional Shape on Soil Reaction (Not Considered in LPILE)

Effect of the Footing Flexural Rigidity (EI) on the Distribution of the Soil Reaction

(Effect of pile/shaft on soil reaction, i.e. p-y curve, which is not accounted in the LPILE p-y curve)

q per unit area

B

CL

q

0.5q

Kr =

Kr = 0

Rigid Footing, Kr =

Flexible Footing, Kr = 0

Footing

H

(1-2s) EP H3

6 (1-2P) Es B3

Kr =

As presented by Terzaghi (1955) and Vesic (1961)

The traditional p-y curve (in LPILE) does not account for the pile/shaft EI variationB

ased

on

th

e S

trai

n

Wed

ge M

odel

An

alys

isS tif f P ile F lex ib le P ile

p -y C u rv e a t a D ep th o f 1 .2 2 m

D en se S an d

L o o se S an d

E f f ec t o f P ile B en d in g S tif f n e ss o n th e p -y C u rv e in S an d

0 4 0 8 0 1 2 0

P ile D e f le c tio n , y , m m

0

1 0 0

2 0 0

3 0 0

4 0 0

Soi

l-P

ile

Rea

ctio

n, p

, kN

/ m EI

0.1 EI

F ree -H ea d P ileF ix ed -H ea d P ile

E ffect o f P ile -H ea d C o n d itio n s o n th e p -y C u rv e in S a n d

p -y C u rv es a t 1 .2 2 -m D ep th

D en se S a n d

L o o se S a n d

0 40 80 120P ile D eflec tio n , y , m m

0

200

400

600S

oil-

Pile

Rea

ctio

n, p

, kN

/ m

Pile/shaft-head condition, which is not considered in the traditional p-y curve

(LPILE) has been proven experimentally and shown below by the SW model

A COMPARISON BETWEEN THE SW MODELAND LPILE COMPUTER PROGRAM

S-SHAFT (SW Model)p-y curve is based on the concept of triaxial test and effective stress analysis, and local site conditions.

p-y curve is a function of pile properties such as pile head fixity, bending stiffness, pile head embeddment, and pile cross-section shape.

LPILESemi-empirical p-y curve based on one full scale field test (Mustang Island test for p-y curve in sand, Sabine River test for soft clay).

p-y curve accounts for only the pile width (no pile properties). The p-y curve is unique in the same soil and for the same pile width.

P-y curve (i.e. modulus of subgrade reaction, Es) is the key factor in the analysis of laterally loaded piles

S-SHAFT (SW Model)

p-y curve for liquefiable soils (completely and partially liquefied soils).

P-y curve for large diameter short shaft P-y curve is affected by the nonlinear behavior of pile material (varying EI).

Mobilized group interaction with no need for assuming any P-multiplier.

LPILE

No p-y curve in liquefied soil. It is just a reduction factor based on soil residual strength

P-y curve for slender long piles

Varying EI has no effect on the p-y curve.

Empirical P-multiplier with pile group.

A number of correction factors

h =

0.6

9 X

o

Xo

Zero Crossing

Xo >

h >

0.6

9 X

o

Xo

Zero Crossing

Zero Crossing

h =

Xo

Def

lect

ion

Patte

rn

Linea

rized

Def

lectio

n

Yo Yo Yo

Li

near

ized

Def

lect

ion

Def

lect

ion

Patte

rn

Long ShaftL/T 4

Intermediate Shaft4 > L/T > 2

Short ShaftL/T 2

L = SHAFT LENGTHT = (EI/f )0.2

f = Coefficient of Modulus of Subgrade Reaction

Varying Deflection Patterns Based on Shaft Type

z

T

y

p

Soil-Shaft Horizontal Resistance

Soil-Shaft Shear Resistance

Tip Reaction Due to Shaft Rotation

Fig. 2. A Model for A Lat erally Loaded Drilled Shaft (Short or Intermediate)

Neglected with Long Shafts

LARGE DIAMETER SHORT SHAFT

Elements Required to Analyze the Large Diameter Shaft:

• Vertical side shear Sand, Clay, C- Soil, Rock

• T-Z Curve Sand, Clay, C- Soil, Rock

• Tip Resistance

• Material Modeling

• Soil Liquefaction

PoMo

Pv

Z

S o i l - S h a f t S id e S h e a r R e s i s t a n c e

Po o

Moo

Pvy

FP

v

v

Mt

Fv

FP

FP

Fv

Fv

Vt

Ft

SHORT SHAFT MODELING

Deformations in soil layers around an axially loaded shafts

Qo

QT

Sheared soil layersLoading Direction q

X

XVert. Shear Stress distribution

Shaft Cross Section

Shaft Vertical Displacement, Z

Sh

ear

Str

ess,

T T-Z curve

o

n

Shaft

r

or

nrn +

m

Displacement, z

zmax

Distancen + m

z

n

Zn +

m

Shear Stress,

Vertical Shear Stress

Shaft Cross Section

The Basic Strain Wedge Model in Uniform Soil

Program Capabilities

• Analysis of short shafts under lateral and axial loads based on soil-shaft-interaction in sand, clay, c- soil and rock (deflection, moment, shear force, line load and excess water pressure)

• p-y curve based on soil and shaft properties• Effect of nonlinear behavior of shaft

material on the p-y curve• Vertical side shear resistance • p-y curve in liquefied soil

• Mobilized t-z curve and shaft base resistance

Program Capabilities

• Shaft group (one row) with/without cap effect

• Shaft classification (short / intermediate/long)and varying cross section

• Isolated shaft-head or shaft group stiffnesses matrix (K11, K22, K33, K44, K55, K66)

• Shaft Axial response (Load vs. Settlement)

COMPARISONS WITH FIELD TESTS

8-ft Diameter Shaft

Table 7 - Soil Profile for the Las Vegas TestSoil layer Soil type Thickness (ft) (pcf) (deg.) k (pci)Layer 1 Sand 2.5 120 33 15Layer 2 Sand 6.5 120 37 30Layer 3 Sand 3.0 120 32 11Layer 4 Sand 1.5 120 36 26Layer 5 Sand 7.5 120 45 62Layer 6 Sand 2.0 120 40 43Layer 7 Sand 3.5 120 45 63Layer 8 Sand 6.0 120 40 44Layer 9 Sand 1.0 120 32 10Layer 10 Sand 2.0 120 37 32

Table 8 – Comparison of Measured Shaft Head Deflection and S-Shaft and FLPIER/COM624P Predictions for LasVegas Test

Load(kips)

Actual shaft-head deflection,Yo, in

S-Shaft Deflection,Yo, in.

FLPIER/COM624 Deflection,Yo, in

50 0.02 0.02 0.201100 0.04 .05 0.402150 0.07 .08 0.603200 0.125 0.11 0.804300 0.235 0.18 1.27400 0.40 0.28 1.89500 0.61 0.41 2.76600 0.88 0.71 3.9700 1.21 1.03 5.75750 1.36 1.2 7.15

0 2 4 6 8Shaft-H ead Latera l D eflection, Y o, in .

0

200

400

600

800

Sh

aft-

Hea

d L

ate

ral L

oad

, Po

, Kip

s

M easuredS-ShaftFLP IER /C O M 624P

Las Vegas field test for short shaft

4-ft Diameter Shaft

Table 9 - Soil Data for Southern California TestSoil layer Soil type Thickness (ft) (pcf) (deg.) Su (psf)

50**Layer 1 Clay 22 130 34 5500 0.0095

Table 10 - Comparison of Measured Shaft Head Deflection and S-Shaft andCOM624P Predictions for Southern California Test

Load(kips)

Actual shaft-head deflection,Yo, in

S-Shaft Deflection,Yo, in.

COM624 Deflection,Yo, in

50 0.1 0.094 0.20100 0.25 0.2275 0.35200 0.67 0.59 1.50300 1.10 1.12 4.40400 1.85 1.74 15.0

Southern California field test for short shaft

0 1 2 3 4 5S haft-H ead Latera l D eflection , Y o, in .

0

100

200

300

400

Sh

aft-

Hea

d L

ater

al L

oad

, Po

, Kip

s

M easuredS-ShaftFLP IER /C O M 624P(L inear analysis)

SHAFT GROUP INTERACTION

P-multiplier (fm) concept for pile group (Brown et al. 1988)

PILE GROUP

Configuration of the Mobilized Passive Wedges,and

Associated Pile Group Interference

S o il S tra in =

3

22

P assiv e S o il W ed g es

P ile in Q u es tio n

T h e In itia l In te rf e ren ce A m o n g P ile s in a P ile G ro u p a t a G iv en D ep th

P ile T y p e 1

P ile T y p e 2

P ile T y p e 3

P ile T y p e 4

Horizontal (Lateral and Frontal ) Interference for a Particular Pile in the Pile Group at a Given Depth (in the Strain Wedge Model)

-0 .5 m0.0 m

3.0 m

8.0 m

12.0 m

17.0 m

25.0 m

32.0 m

= 35 o

= 19 kN /m 3

= 35 o

= 9.2 kN /m 3

= 34o

= 9.4 kN /m 3

= 34o

= 9.2 kN /m 3

S u=121.3 kN /m 2

= 9.2 kN /m 3

50 = 0.005

S u=115 kN /m 2

= 9.2 kN /m 3

50= 0.005

S u=60 kN /m 2

= 9.2 kN /m 3

50= 0.007

Sand

S and

Sand

Sand

C lay

C lay

C lay

Free head pile

a) O rig inal so il p ro file

4.5 m

Loading D irection

b) S ix 1 .5-m -D iam eter Bored P ile G roup (F ixed H ead)

Shaft B1

Shaft B2

The Taiwan Test by Brown et al. 2001

In order to match the measured data using LPILE, the traditional p-y curves were modified as shown above

0 40 80 120 160 200P ile H ead D eflection, Y o, m m

0

1000

2000

3000

4000

Pile

He

ad

Lo

ad

, Po,

kN

Measured (Brown et al. 2001)Predicted (SW Model)No V. Side ShearW ith V. Side Shear

Single 1 .5-m -D iam eter Bored P ile (B 1)

Free-head

0 10 20 30 40C ap D eflection, Y g, m m

0

4000

8000

12000

Pile

Gro

up

Lat

era

l Loa

d, k

N

Measured (Brown et al. 2001)Predicted (SW Model)

Latera l R esponse of a (3 x2) P ile G roup

Fixed head

SHORT SHAFTS IN LIQUEFIED SOIL

Current Available Procedures That Assess the Pile/Shaft Behavior in Liquefied Soils (Using the Traditional P-y Curve):

1. Construction of the p-y curve of soft clay based on the residual strength of liquefied sand presented by Seed and Harder (1990)

2. The use of random Pmult < 1 to reduce the stiffness of the traditional p-y curve of sand

3. Reduce the unit weight of liquefied sand with the amount of Ru (Earthquake effect in the free-field ) and then build the traditional p-y curve of sand based on the new value of the sand unit weight. (proposed by Brown based on Cooper River Test)

0 4 8 12 16 20 24Equivalent Clean Sand SPT Blowcount, (N1)60-CS

0

400

800

1200

1600

2000

Res

idu

al U

nd

rain

ed

Sh

ear

Str

eng

th, S

r (p

sf)

E a rth q u a k e -In d u ce d L iq u efac tio n a n d S lid in g C a se H is to r ie s W h e reS P T D a ta & R es id u a l S tre n g th P a ra m e te rs H a v e b e e n M e asu re d

E a rth q u a k e -In d u ce d L iq u efac tio n a n d S lid in g C a se H is to r ie s W h e reS P T D a ta & R es id u a l S tre n g th P a ra m e te rs H a v e b e e n E s tim a ted

C o n stru c tio n -In d u c ed L iq u efa tio n a n d S lid in g C a se H is to rie s

L o w er S a n F ern a n d o D a m

Fig. 1 Corrected blowcount vs. residual strength (Seed and Harder, 1990)

Pile Deflection, y

Soi

l-P

ile

Rea

ctio

n, p

Measured p-y Curves atTreasure Island Test (Rollins and Ashford)

Upper Limit of Sr using soft clay p-y curve

Lower Limit of Sr

API Procedure

Comparison between the actual p-y curve in liquefied soil and the currently used ones

Post-liquefaction stress-strain behavior of completely liquefied sand (uc = 3c and Ru =1)

Axial Strain,

Dev

iato

r S

tres

s,

dPost-liquefaction stress-strain behavior of partially liquefied sand (uc < 3c and. Ru <1)

xo

d = 2 Sr

Fig. 1 Subsequent undrained stress-strain behavior of sand that has experienced partial or complete liquefaction (employed in S-Shaft)

Input Data Utilized in the SW Model Procedure (S-SHAFT):1. Peak ground acceleration (amax) and the magnitude

of the EQ to evaluate the excess porewater pressure (Ru) induced by cyclic loading

2. Pile/Shaft properties

3. Soil properties:Effective unit weight of soil(N1)60 (i.e Relative density, Dr) Angle of internal friction ()Sand grain roundness parameter (

Percentage of finesAxial strain in sand at 50% strength, 50%

Uniformity coefficient (Cu)

TABLE I. SOIL PROPERTIES EMPLOYED IN THE SWM ANALYSIS FOR TREASURE ISLANDTEST

Soil LayerThick. (m)

Soil Type Unit Weight, (kN/m3)

(N1)60 φ(degree)

ε50

%*Su

kN/m2

0.5 Brown, loose sand (SP) 18.0 16 33 0.45

4.0 Brown, loose sand (SP) 8.0 11 31 0.6

3.7 Gray clay (CL) 7.0 4 1.5 20

4.5 Gray, loose sand (SP) 7.0 5 28 1.0

5.5 Gray clay (CL) 7.0 4 1.5 20

* Undrained shear strength

Peak Ground Acceleration (amax) = 0.1 gEarthquake Magnitude = 6.5 Induced Porewater Pressure Ratio (ru) = 0.8 - 0.9

Soil Profile and Properties at the Treasure Island Test

P ile H ead E levation ( 0 .00 )P o

M o = 0 .0

A xia l Load= 0.0

D iam eter of P ile

Pile

Le

ngt

h =

20

.0 ft

Thickness of Layer # 2


W ater Tab le

SA

ND

CL

AY

G round Surface1.0 m

4.0

m4.

0 m

0 .61 m

Layer th ickness = 4.0 mE ffective un it w e ight = 8 .0 kN /m 3

E ffective fric tion ang le = 31.0o

e50 = 0 .006, (N 1)60 = 11

Layer th ickness = 3.7 mE ffective un it w e igh t = 7 .0 kN /m 3

E ffective fric tion ang le = 24 o o r 0 .0 (defau lt)(S u)Top =20 kN /m 2, (S u)B o ttom =20 kN /m 2

e50 =0.015

CL

AY

SA

ND

4.5

m7.

5 m

0 .5 m


Layer th ickness = 5.0 mE ffective un it w e ight =7 .0 kN /m 3

E ffective fric tion ang le =28.0o

e50 = 0 .01, (N 1)60 = 9

Layer th ickness = 5.5 mE ffective un it w e igh t = 7 .0 kN /m 3

E ffective fric tion ang le = 24 o o r 0 .0 (defau lt)(S u)Top =20 kN /m 2, (S u)B o ttom =20 kN /m 2

e50 =0.015



Layer th ickness =0.5 mE ffective un it w e igh t = 18.0 kN /m 3

E ffective fric tion ang le =33.0o

e50 = 0 .0045, (N 1)60 = 16

% of fines= 5%

% of fines= 10%

T-Shell

P eak G round Acceleration (a m ax) = 0 .1gM agnitude of E arthquake = 6.5N o la tera l spreadingFree- and N ear-fie ld excess porew ater pressure e ffectA ssum e sand grains Subangular

Shaft SectionN um bers of shaft segm ents =1Segm ent length = 20 mShaft d iam eter = 0 .61mSteel shell th ickness = 9 .5 m mfy o f the steel shell = 420000 kN /m 2

fc of concrete = 34444 kN /m 2

fy o f the steel bars = 420000 kN /m 2

R atio of S teel bars (A s/A c)= 2%R atio of Transversesteel = 0.3%

Shaft W idth

x x

Longitud ina l S tee l

TREASURE ISLAND TEST

O b se rv ed

P red ic ted

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0P ile -H ead D e flec tio n , Y o , m m

0

40

80

120

160P

ile-

Hea

d L

oad,

Po,

kN C IS S , 0 .3 2 4 m

E I = 4 4 5 1 5 k N -m 2

N o -L iq u efac tio nP o st-L iq u e fac tio n

(u x s , ff + u x s , n f)

Measured and Calculated Results for Treasure Island Test (CISS of 0.324-m diameter

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0P ile-H ead D ef lectio n , Y o , m m

0

40

80

120P

ile-

Hea

d L

oad,

Po,

kN H -P ile , 0 .3 1 0 m

E I = 4 9 0 0 0 k N -m 2

O b se rv ed

P red ic ted

No-

Liq

uefa

c tio

n

P o st-L iq u e fac tio n

(u x s , ff + u x s , n f)

Measured and Calculated Results for Treasure Island Test (H-Pile)

0 1 0 0 2 0 0 3 0 0 4 0 0P ile -H ead D ef lectio n , Y o , m m

0

100

200

300

400

500

Pil

e-H

ead

Loa

d, P

o, k

NC IS S , 0 .6 1 mE I = 4 4 8 3 2 0 k N -m 2

O b serv edP red ic ted (S W M )P red ic ted (C o m 6 2 4 )

No -

L iqu

e fac

tion

P o s t-L iq u e fa c tio n (u x s , ff + u x s , n f)

Measured and Calculated Results for Treasure Island Test (CISS of 0.61-m diameter

0 4 8 12 16 20 24Equivalent Clean Sand SPT Blowcount, (N1)60-CS

0

400

800

1200

1600

2000

Res

idu

al U

nd

rain

ed

Sh

ear

Str

eng

th, S

r (p

sf)

E a rth q u a k e -In d u ce d L iq u efac tio n a n d S lid in g C a se H is to r ie s W h e reS P T D a ta & R es id u a l S tre n g th P a ra m e te rs H a v e b e e n M e asu re d

E a rth q u a k e -In d u ce d L iq u efac tio n a n d S lid in g C a se H is to r ie s W h e reS P T D a ta & R es id u a l S tre n g th P a ra m e te rs H a v e b e e n E s tim a ted

C o n stru c tio n -In d u c ed L iq u efa tio n a n d S lid in g C a se H is to rie s

L o w er S a n F ern a n d o D a m

Fig. 1 Corrected blowcount vs. residual strength (Seed and Harder, 1990)

0 40 80 120 160P ile Latera l D eflection, y (m m )

0

20

40

60

80p

(kN

/m)M easured P redicted (SW M odel)

API (Pmult = 0.3)

p-y Curve at 0.2 m Below Ground (0.61-m Diameter CISS )

The SW Model is the only program to predict the concave-up p-y curve at Treasure Island Test

0 40 80 120P ile Latera l D eflection, y (m m )

0

10

20

30

40

50p

(kN

/m)

M easured P red icted (SW M odel)

API (Pmult = 0.3)


0 40 80 120P ile Latera l D eflection, y (m m )

0

10

20

30

40

50p

(kN

/m)

M easured P red icted (SW M odel)


API (Pmult = 0.3)

Treasure Island - CISS 0.61p-y CURVE OF SINGLE PILE (FREE-HEAD)

1.2 m2.5 m3.3 m4 m4.8 m

Soil-

Pile

Rea

ctio

n, p

, kN

/m

Pile Deflection, y, mm

0

10

20

30

40

50

60

0 50 100 150

P-y curves from the SW model program

Peak Ground Acceleration (amax) = 0.3 gEarthquake Magnitude = 6.5 Induced Porewater Pressure Ratio (ru) = 1.0

Mt. Pleasant Site (Cooper River Br) Soil Profile and Data Input

TABLE II. SOIL PROPERTIES EMPLOYED IN THE SW MODEL ANALYSISFOR COOPER RIVER BRIDGE TEST AT MT. PLEASANT

Soil LayerThick. (ft)

Soil Type Unit Weight, (pci)

(N1)60 φ(degree)

ε50

%*Su

psf4 Slightly clay

sand (SP-SC)120 19 34 0.004

9 Sandy clay (CH) 62 7 30 0.00816 Very clayey

sand (SC-CL)62 10 32 0.006

9 Silty sand (SM) 62 7 30 0.00880 Cooper Marl 65 20 0.002 4300

Soil Profile and Properties at the Cooper River Bridge Test

0 1 2 3 4 5Latera l S haft-H ead D isp lacem ent, Y o, in .

0

400

800

1200

La

tera

l Lo

ad

, Po

, kip

s

MeasuredLPILE (Input p-y curve from O -Cell )SW Model

Static LoadPostliquefaction

am ax = 0.1g

am ax = 0.3g

R andomru = 0 .7

Lateral response of shaft MP-1 at Mount Pleasure test site (Cooper River Bridge)

Induced ru in the field = 1.0

, ru = 1

Documents

JP Singh and Associates in association with Mohamed Ashour, Ph.D., P.E. Gary Norris, Ph.D., P.E. March 2004 COMPUTER PROGRAM S-SHAFT FOR LATERALLY LOADED