Method for Prediction of Micropile Resistance for Slope Stabilization

J. Erik Loehr, Ph.D., P.E.University of Missouri

Dan A. Brown, Ph.D., P.E.Auburn University

2007 International Workshop on MicropilesToronto, OntarioSeptember 27, 2007

2

Limit States for Soil Reinforcement

Geotechnical failure• passive failure (lateral) above or below sliding

surface• pullout failure (axial) above or below sliding

surfaceStructural failure• flexural failure• shear failure• axial failure

- compression- tension

Serviceability limits

3

Proposed Approach

Estimate/assume profile of soil movementResolve soil movement into axial and lateral componentsPredict mobilization of axial and lateral resistance• Using “t-z” analyses for axial load transfer• Using “p-y” analyses for lateral load transferSelect appropriate axial and lateral resistance with consideration given to movement required to mobilize resistance

4

Soil Movement Components− θ+ θ

Slope Surface

θ

θ

SlidingSurface

δaxial lat.δ

δsoil

lat.δ δaxial

soilδ

5

t-z analyses for axial resistance

Transition (Sliding) Zone

z

axialδ

Input Profile of Axial Soil Movement

Pile Axial Stiffness (EA)

Soil Shear Resistance (t)

Soil End Bearing (Q)

Cap Bearing

Sliding Surface

Axial Componentof moving soil

Stable Soil(no soil movement)

6

Mobilization of Axial Resistance

clay

rock

slide

0

10

20

30

40

50

0 20 40 60 80 100 120 140 160Mobilized Axial Load (kip)

Depth

(ft)

d=0.1 ind=0.3 ind=0.42 ind=0.5 in

Upslope MicropileSliding Depth = 33-ft

7

Mobilization of Axial Resistance

0

50

100

150

200

250

300

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Total Slope Movement (in)

Mobil

ized A

xial F

orce

(kip)

10-ft33-ft40-ft

Upslope Micropile

8

Axial Resistance Function

clay

rock

0

10

20

30

40

50

0 20 40 60 80 100 120 140 160 180 200Axial Resisting Force (kip)

Slidi

ng D

epth

(ft)

Upslope Micropile

9

p-y analyses for lateral resistance

Transition (Sliding) Zone

z

latδL-Pile Model

Input Profile of Lateral Soil Movement

Pile Bending Stiffness (EI)

Soil Lateral Resistance (p)

Sliding Surface

Lateral Componentof moving soil

Stable Soil(no soil movement)

10

Mobilization of Lateral Resistance

clay

rock

slide

0

10

20

30

40

50

0.0 1.0 2.0 3.0 4.0 5.0Pile Deformation (in)

Depth

(ft)

0

10

20

30

40

50

-1500 -750 0 750 1500Mobilized Bending Moment (kip-in)

0

10

20

30

40

50

-80 -40 0 40 80Mobilized Shear Force (kip)

d=0.1 ind=1.0 ind=3.0 in

11

Mobilization of Lateral Resistance

0

200

400

600

800

1000

1200

1400

1600

0.0 2.0 4.0 6.0 8.0 10.0Total Slope Movement (in)

Mobil

ized B

endin

g Mom

ent (

in-kip

)

z=10-ftz=33-ftz=45-ft

Upslope Micropile

0

20

40

60

80

100

120

140

160

0.0 2.0 4.0 6.0 8.0 10.0Total Slope Movement (in)

Mobil

ized S

hear

For

ce (k

ip)

z=10-ftz=33-ftz=45-ft

Upslope Micropile

12

Lateral Resistance Function

clay

rock

0

10

20

30

40

50

0 20 40 60 80 100 120 140 160Lateral Resisting Force (kip)

Slidi

ng D

epth

(ft)

Ultimated<1-in

Upslope Micropile

13

Example Problem

14

Example – with Micropiles

Micropiles battered at

+/- 45º

15

Example Problem

16

Stresses on sliding surface

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

-200 -150 -100 -50 0 50X coordinate (ft)

Stre

ss (p

sf)

Effective Normal Stress (psf)Mobilized Shear Resistance (psf)

decrease in stress dueto downslope pile

increase in stress dueto upslope pile

17

Comparison with measured resistance

Compared resistance predicted using proposed method with measured values• Mobilized axial resistance• Mobilized bending momentsUsed measured values for:• Soil strength• Pore water pressures• Soil deformationsDeveloped “best match” using “p-modifiers” and “t-modifiers”

18

Modified p-y curves

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Lateral Deflection, y (in)

Later

al Lo

ad In

tensit

y, p

(kip/i

n)

p mob = 2.0

p mob = 1.0

p mob = 0.5

p mob = 0.25 p mob = 0.05

Soft Clay Model s u = 2,000 psf ε 50 = 0.02 z = 30-ft

19

Modified t-z curves

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Axial Deflection, z (in)

Axial

Load

Inten

sity,

t (kip

/ft)

α = 2.0

α = 1.0

α = 0.5 α = 0.3 α = 0.1

Soft Clay Model s u = 2,000 psf z ult = 0.06-in = 0.01*d

20

Littleville Alabama Case

21

Mobilized Bending Moments – Littleville

0

10

20

30

40

50

-40 -20 0 20 40Bending Moment (in-kips)

Depth

(ft)

predictedmeasured (2+70U)measured (1+70U)

δ tot = 0.39-in

upslope p mod = 0.2

0

10

20

30

40

50

-40 -20 0 20 40Bending Moment (in-kips)

Depth

(ft)

predictedmeasured (2+70U)measured (1+70U)

downslope p mod = 0.2

δ tot = 0.31-in

22

Mobilized Axial Resistance – Littleville

0

10

20

30

40

50

-60 -40 -20 0 20 40 60Axial Load T, kip (+=tension)

Depth

, z (f

t.)

predictedmeasured (2+70U)measured (1+70U)δ tot = 0.24-in

downslopeα = 0.3z ult = 0.06-in

0

10

20

30

40

50

-60 -40 -20 0 20 40 60Axial Load T, kip (+=tension)

Depth

, z (f

t.)

predictedmeasured (2+70U)measured (1+70U)

δ tot = 0.34-in

upslopeα = 0.3z ult = 0.06-in

23

Summary of evaluations

Comparison of measured and predicted forces reasonableBUT…must use modified p-y and t-z modelsPossible reasons: • Drained vs. undrained loading• Group and/or scale effects• Softening of pile-soil interface• Pile inclination• Error/bias in measurements:

- Shear strength parameters- Soil movement

• Others???

24

Predicted Mobilization – Littleville

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

0 5 10 15 20Total Slope Movement (in)

Mobil

ized S

hear

For

ce (k

ip)stiff clay modelAPI sand modelalternatecalibration points

Upslope MicropileSlide Depth = 33-ft

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

0.0 1.0 2.0 3.0 4.0Total Slope Movement (in)

Mobil

ized A

xial F

orce

(kip)

prediction Aprediction A*calibration points

Upslope MicropileSliding Depth = 33-ft

25

Large-scale Model Tests

26

Large-scale Model Tests

27

0

5

10

15

20

25

30

-300 -200 -100 0 100 200 300Induced Bending Moment (lb-in)

Posi

tion

Alo

ng P

ile (i

n. fr

om b

otto

m)

44 (2.8)LPile (2.8)

0

5

10

15

20

25

30

-1000 -500 0 500 1000Induced Axial Load (lb)

Posi

tion

Alo

ng P

ile (i

n. fr

om b

otto

m)

44 (2.8)t-z (2.8)

TC

Model vs. measurement – no cap

Test 2-A, Member 3 (downslope), S/D=10

28

Model vs. measurement – with cap

0

5

10

15

20

25

30

35

40

45

-1000 -500 0 500 1000Induced Axial Load (lb)

Posi

tion

Alo

ng P

ile (i

n. fr

om b

otto

m)

44 (1.9)t-z (1.9)

TC

0

5

10

15

20

25

30

35

40

45

-1500 -500 500 1500Induced Bending Moment (lb-in)

Posi

tion

Alo

ng P

ile (i

n. fr

om b

otto

m) 44 (1.9)

LPile (1.9)

Test 3-A, Member 2 (upslope), S/D=10

29

Conclusions

Proposed uncoupled method suitable for predicting micropile resistance when cap influence is limitedUse of modified p-y and t-z models requiredWhen cap interaction is significant, uncoupled method does not accurately predict responseFull axial resistance frequently mobilized at relatively small soil movementsFull lateral resistance frequently not mobilized without substantially greater soil movementsAdditional data needed!!!

30

AcknowledgementsADSC/DFI Micropile CommitteeADSC Industry Advancement FundNational Science Foundation Grant CMS0092164Many students…