Dipl.-Ing. Stefan Vogt Zentrum Geotechnik, Technische Universität München

Buckling of slender piles in soft soils –

Large scale loading tests and introduction of a simple calculation scheme

Research work at the Zentrum GeotechnikMotivation

load

firm soil layer

slender piles

foundation

weicheBodenschicht(very) soft soil layer

Has buckling to be expected ?

Are the standards requirements save enough?

EC 7:„.. check for buckling is not required if cu exceeds 10 kPa..“

Other codes set this limit of undrained shear strength at 15 kPa or 10 kPa(eg. DIN 1054, 2005 or the national technical approvals for micropiles)

Research work at the Zentrum GeotechnikMotivation

We asked:

Are the published design methods capable to simulate the interaction between the supporting soil and the pile?

Research work at the Zentrum GeotechnikMotivation

Reviewed papers:

Vik (1962), Wenz (1972), Prakash (1987), Wennerstrand&Fredriksson (1988), Meek (1996), Wimmer (2004), Heelis&Pavlovic&West (2004)

We asked:

2.) An elastic approach to describe the lateral soil support is not appropriate

Summary of the results obtained in the first step

1.) The standards rules underestimate the possibility of pile buckling

3.) Most published calculation methods cannot simulate the pile‘s behavior properly

Literature research

In situ field load test

Model scaled tests

Large scaled loading tests

Development of a simple design method

Development of a numerical FE-Model Reported by Prof. N. Vogt at the IWM 2004 in Tokyo

Research work at the Zentrum GeotechnikIntroduction

Aim:

Proofing the obtained expertise with large scaled loading tests on single piles

Development of a simple design method that can simulate the main effects recognized in the loading tests

Literature research

In situ field load test

Model scaled tests

Large scaled loading tests

Development of a simple design method

Development of a numerical FE-Model

Research work at the Zentrum GeotechnikIntroduction

Large scaled loading testsLoading of 4 m long single piles

Container made up with concrete segments

Pile is pinned top and bottom

axial loading forcesettlement of

the pile head

1,0 m

1,0 m

1,0 m

1,0 m

lateral deflection

lateraldeflection

lateraldeflection

4,0 m

Measuring devices

Large scaled loading testsLoading of 4 m long single piles

Container made up with concrete segments

Mixing up the soil in a liquid consistency

Filling the containers by pumping the liquid soil – following consolidation with the help of the electro osmotic effects

Draining system

Pumping the liquid soil

Large scaled loading tests

necessary settlement

bridge abutment

hydraulicjack

test pile

rigid foundation

geotextiledrainage

surchargeload

necessary settlement

bridge abutment

hydraulicjack

test pile

rigid foundation

geotextiledrainage

surchargeload

Pile type I:Composite cross section GEWI28Steel rod d = 28 mm Hardened cement slurry D = 100 mm

Pile type II:Aluminum profileThickness = 40 mmWidth = 100 mm

Large scaled loading tests

Large scaled loading tests

Exemplary illustration of a loading test:

Alu-pile surrounded by a supporting soil of cu = 18 kPa

Statistical analysis:

maximum shear strength

residual shear strength

Large scaled loading testsShear vane tests: Soil support of cu = 18 kPa

Maximum shear resistance cfv

= 18,7 kN/m2

= 2,1 KN/m2Mean valueStandard deviation

Residual shear strength cRv

= 12,7 kN/m2

= 1,2 KN/m2Mean valueStandard deveation

Normal plastic clay TMw = 40,8..42,1 %Ic = 0,53..0,48

0 10 20 30 40undrained shear strength cu [kPa]

0

25

50

75

100

125

150

175

200

225

250

0 600 1200 1800 2400 3000 3600 4200 4800 5400 6000 6600 7200 7800 8400 9000

Meßdauer [s]

Pfah

lnor

mal

kraf

t N [k

N]

0

4

8

12

16

20

Vers

chie

bung

am

Pfa

hlko

pf u

O [m

m]

Pfahlnormalkraft

Verschiebung uo

Querschnitt:

Versuchsnummer: KFL-FLACH40x100-02 System:

uO

N

A

Large scaled loading testsLoading characteristic: Soil support of cu = 18 kPa

Settlement of the pile head

Sudden increase of the pile head settlement while the axial normal force is decreasing

time [s]

settl

emen

t of t

he p

ile h

ead

[mm

]

axia

l pile

forc

e [k

N]

No sign in the characteristic of the measured deformations that showed the pile failure in advance!

Large scaled loading testsLateral deflection: Soil support of cu = 18 kPa

Axial force N deflection w

N

220 kN (ultimate) 9 mm

212 kN 1,2 mm

100 kN 0,9 mm

50 kN 0,4 mm

ww

Large scaled loading testsAnalysis

Results:

- With an increasing soil’s undrained shear strength cuthe ultimate bearing capacity rises

0

50

100

150

200

250

300

350

400

450

500

0 5 10 15 20 25cu [kN/m2]

N [k

N]

pile type I (Ep·Ip = 55 kNm2)

pile type II (Ep·Ip = 38 kNm2)

600plastic normal force pile type II

plastic normal force pile type I- Buckling regularly determined the ultimate state of the system, even in soils with an undrained shear strength of cu > 15 kN/m2

0,0

200,0

400,0

600,0

800,0

1000,0

0,00 2,00 4,00 6,00M [kNm]

N [k

N]

cu = 0 kN/m2

cu = 10,5 kN/m2

cu = 18,7 kN/m2

Interaktionskurve des Pfahles FLACH40x100

Large scaled loading testsAnalysis

Results:

No failure due to a limited pile‘s material strength!

maximum interaction of the internal force variables (pile type II)

??Even the backing moment

out of the lateral soil support is not considered

Large scaled loading testsAnalysis

For lower axial forces the lateral deflections of the pile remain very little (stiff behavior)

The failure of the micro piles occurred suddenly (no sign of failure from the measured deformations)

The halve waves of the buckling pile‘s bending curve were always smaller than the full pile‘s length (from joint to joint)

Results:

Introduction of a simple design method

Substituted mechanical system with a buckling length of LHw

an infinite long pile can be assumed for the calculations;

N

z

the length of the effective buckling figure’s half wave LHw can develop freely for the most conditions in situ at the upper and lower boundaries of the soft soil layer

LHw

Introduction of a simple design methodFinding a static system

the large scaled loading tests showed that the length of the buckling figure’s half waves were smaller than the maximum possible length of 4 m;

All forces acting on the static system with a length of LHw

z

LHwLHwp(z)

P

zp

Lateral soil support

w0,M

N

N

wN,M

MM

Bending moment in the middle

T = P

T = 0

Introduction of a simple design methodFinding a static system

Setting up equilibrium:

z

LHwLHwp(z)

P

zp

w0,M

N

N

wN,M

MM

T = P

T = 0

Condition ∑M = 0 at the pinned top

pHw

M,NM zPimpLwNM ⋅−

+⋅=

Introduction of a simple design methodDerivation

Force from the lateral soil support is defined piecewise in order to a elastic-plastic soil resistance

z

LHwLHwp(z)

P

zp

w0,M

N

N

wN,M

MM

T = P

T = 0

Force P from a bi-linear approach of the supporting soil:

π⋅⋅= Hw

M,NlLwkP for: wN,M < wki

deformation wN,M

supportion force P

wki

kl

1

Introduction of a simple design methodDerivation

for: wN,M ≥ wkiπ⋅⋅= Hw

kilLwkP

pffor a deformation of wN,M > wkithe lateral supporting force is remaining constant

Condition ∑M = 0 at the pinned top

pHw

M,NM zPimpLwNM ⋅−

+⋅= ″⋅⋅−= M,NppM wIEM

Assumption: The pile‘s material remains elastic

impLw

Lp1IEL

wN

HwM,N

2HwM2pp2

Hw

2

M,N

+

⋅⋅π

+⋅⋅π⋅=

defined picewise

Introduction of a simple design methodDerivation

wN,M

N

wki

buckling load according to ENGESSER (elastically bedded beam):

buckling load according to EULER (unsupported beam):imperfect unsupported beam

perfect unsupported beam

impLw

Lp1IEL

wN

HwM,N

2HwM2pp2

Hw

2

M,N

+

⋅⋅π

+⋅⋅π

⋅=

N = F (wN,M, Ep·Ip, imp, LHw and the soil support: pf and wki)

Introduction of a simple design methodPresentation

imperfect elastically bedded beam

perfect elastically bedded beam

perfect bilinear bedded beam

imperfect bilinear bedded beam

LHw is unknown!

For defined parameters (soil support, imperfection and flexural rigidity) there is one length of LHw, for which the buckling load Nki is minimal

LHw

Nki

effective LHw

effective Nki

impLw

Lkw1IEL

wN

Hwki

2Hwlki2pp2

Hw

2

ki

ki+

⋅⋅⋅π

+⋅⋅π

⋅=

Introduction of a simple design methodPresentation

Vary LHw to find the minimum and therefore effective buckling length!

1.) Define the parameters of the lateral soil support pf und wki

Summary of the calculation sequence:

2.) Define an imperfection and the flexural rigidity of the pile’s cross section

3.) Evaluate the effective buckling half wave's length LHw

4.) Calculate the buckling load Nki

5.) Check if the pile’s material strength governs the maximum bearing capacity (this means: “does the pile’s material yield before the buckling load is reached”)

You may download an Excel-Sheet at www.gb.bv.tum.de

Introduction of a simple design method

Pile type I

50 mm

hardened cement: C20/25

GEWI28: BSt 500 S100 mm

Used: half side cracked cross section (no tension stresses in the hardened cement)

Ep·Ip = 55 kNm2

0

50

100

150

200

250

300

350

400

450

500

0 5 10 15 20 25cu [kN/m2]

N [k

N]

pf = 6 · cu · b

kl = 60 · cu

imp = 300

pf = 10 · cu · b

kl = 100 · cukl = 100 · cu

imp = 600

Introduction of a simple design methodBack-calculation of the large scaled tests

Alu-pile:

40 mm

Al Mg Si 0,5

100 mm

Ep·Ip = 38 kNm20,0

200,0

400,0

600,0

800,0

1000,0

0 5 10 15 20 25

kl = 70 · cupf = 7 · cu · D

kl = 100 · cupf = 7 · cu · D

kl = 100 · cupf = 10 · cu · D

cu [kN/m2]

N [k

N]

Pile type II

Introduction of a simple design methodBack-calculation of the large scaled tests

Summary

In (very) soft soils pile buckling should always be verified!

With the help of the presented design method the main effects of the loading tests can be considered in basic.

The insecurities upon the design method is based and which are recognizable comparing the theoretical results with the data form the pile load tests must be covered by partial safety factors on the structural part and the soil resistance.

- Compound effects steel-concrete

- Soil resistance (wki, pf)

- Viscous influence creep and relaxation

Thank you for yourAttention!

Literature research

In situ field load test

Model scaled tests

Large scaled loading tests

Development of a simple calculation scheme

Development of a numerical FE-Model

beam supported by springsN

characteristic of the lateral reaction forces

elastisch or elastisch-plastisch

lateral deflection

supporting force

Research work at the Zentrum GeotechnikIntroduction

Loading tests on 80 cm long model piles

Comparison of the test results with the predicted buckling loads (both numerical FEM and published calculation methods)

Varying soil strengths and cross sections

0

20

40

60

80

100

0 5 10 15 20 25 30 35undrainierte Scherfestigkeit cu [kN/m²]

Kni

ckla

st N

k [kN

]elastic characteristic of the springs

buck

ling

load

[kN

]

undrained shear strengh cu [kN/m2]

elastic-plastic characteristic of the springs

Literature research

In situ field load test

Model scaled tests

Large scaled loading tests

Development of a simple calculation scheme

Development of a numerical FE-Model

Research work at the Zentrum GeotechnikIntroduction

Loading test of a GEWI-pile in soft, organic soil

Sudden pile failure at a load very little above the design load

Literature research

In situ field load test

Model scaled tests

Large scaled loading tests

Development of a simple calculation scheme

Development of a numerical FE-Model

Research work at the Zentrum GeotechnikIntroduction

90

Large scaled loading testsResults of the loading tests of three unsupported composite piles

Buckling load of the unsupported pole (EULER II)89 kN

Loading an pile with such an inelastic behavior due to its cross section material (unpredictable crack propagation of the concrete) is improper to qualify the lateral soil support!

0

10

20

30

40

50

60

70

80

100

0 20 40 60 80 100 120 140 160 180 200

Lateral deflection in the middle of the pile wN,M [mm]

Axi

al p

ile fo

rce

N [k

N]

Nu

wu

Nu

wu

Nu

Why to use an aluminum pile?

Large scaled loading testsPile type II: Aluminum profile

Some pile is needed which behaves elastically over a wide range of lateral displacements and which reproduces the buckling load according to EULER in the unsupported case.

Solution: A aluminum pile that has a similar flexural rigidity compared to the cracked composite cross section.

50 mm

Cement: C20/25

GEWI28: BSt 500 S100 mm

Composite cross section, cracked half side

Ep·Ip = 55 kNm2

Aluminum profile

40 mm

Al Mg Si 0,5

100 mm

Ep·Ip = 38 kNm2

Large scaled loading testsTest results obtained by loading of an unsupported alu-pile

0

20

40

60

80

100

120

140

160

180

200

0 600 1200

time [s]

axia

l pile

forc

e N

[kN

]

0

20

40

60

80

100

late

ral d

ispl

acem

ent i

n th

e m

iddl

e of

the

pile

w [m

m]

Ultimate bearing capacity of the unsupported composite-piles:

Nk = 55, 22 und 19 kN

Nk = 22 kN

Alupile:always

Introduction of a simple design methodDerivation

z

LHwLHwp(z)

P

zp

w0,M

N

N

wN,M

MM

T = P

T = 0

⋅

π⋅= z

Lsinw)z(w

HwM,00

Assumption of sinus shaped bending curves

⋅

π⋅= z

Lsinw)z(w

HwM,NN

Assumption of a sinus shaped deformation due to imperfection

This yields to a sinus shaped form of the load per unit length due to the lateral soil support

⋅

π⋅= z

Lsinp)z(p

HwM

Is the decisive buckling load Nki the ultimate axial load Nu of the micropile?

The pile‘s material may yield before the buckling load is reached. In this case the pile‘s material strength governs the ultimate load.

−⋅=

α

plpl N

N1MM

−⋅

⋅⋅π

⋅=

α

plpp2

2Hwpl

pl,M NN1

IELM

w

Introduction of a simple design method

lateral deformation wN,M

axia

l pile

forc

e N

A

B

D

C

wM,pl case 1wM,pl case 2

case 1

case 2