discrete element simulations of granular-shaft interaction

Tang-Tat Ng Department of Civil Engineering

University of New Mexico

Discrete Element Simulations of Granular Soils-Shaft Interaction of

Smooth Drilled Shafts 離散元素法模擬岩土和 鑽孔灌注桩的摩擦力

• INTRODUCTION • MODELS FOR GRANULAR SOILS AND A SHAFT • DISCRETE ELEMENT MODELS • NUMERICAL RESULTS • A FIELD CASE AND COMPARISON • GENERAL FORM OF THE NEW DESIGN EQUATION • CONCLUSIONS

DEM Simulations of Granular Soils-Shaft Interaction of Smooth Drilled Shafts

• THE LOAD RESISTANCE FACTOR DESIGN (LRFD) IS REQUIRED TO DESIGN DRILLED SHAFTS FOR HIGHWAY APPLICATIONS IN THE UNITED STATES

• LOW RESISTANCE FACTORS FOR SIDE RESISTANCE ARE RECOMMENDED DUE TO THE UNCERTAINTY OF THE CURRENT DESIGN EQUATIONS AND OTHER FACTORS

• DEVELOPMENT OF A NEW DESIGN EQUATION OR IMPROVEMENT OF CURRENT DESIGN EQUATIONS CAN LEAD TO BETTER PREDICTION OF SIDE RESISTANCE

• COST SAVING CAN BE ACHIEVED FROM THE NEW DESIGN EQUATION

INTRODUCTION

Drilled Shafts in Highway Application

Drilled Shafts in Highway Application

CONSTRUCTION OF DRILLED SHAFTS

Qu

Qs

Qb

The ultimate bearing capacity (Qu )of a shaft is assumed to be the sum of skin friction and end-bearing resistance:

Qu = Qb + Qs

where Qu total shaft resistance, Qb is the end bearing resistance and Qs is side friction resistance

General behavior Shaft resistance fully mobilized at small shaft movement (<0.01D) Base resistance mobilized at large movement (0.1D)

Bearing Capacity of Drilled Shafts

vi′ = average vertical effective stress of layer i over the depth interval Δz where,

fult = the ultimate unit side resistance (fult 200 kPa) i = 1.5 - 0.244√zi ; N60 ≥ 15 i = (N60/15)*(1.5 - 0.244√zi) ; N60 < 15 i = (0.25 ≤ β ≤ 1.2) N60 = uncorrected SPT blow count, for depth representative of layer i; zi = vertical distance from the ground surface (in m) to the middle of

the layer i; In gravelly sands or gravels and SPT N60 ≥ 15 = 2 - 0.15*zi

0.75, (0.25 ≤ β ≤ 1.8)

Design Equation The O’Neill and Reese Method (1999)

'

viiultf

Design Equation The NHI Method (FHWA 2010)

'

viFultf

tantan)sin1(

sin

'

'

p

v

p

F K

245tan2 o

PK

The preconsolidation pressure, p′, is suggested (Mayne 2007) :

where, m = 0.6 for clean quartzite sands and m = 0.8 for silty sands to sandy silts.

Is suggested (Kulhawy and Chen 2007) as:

= 27.5 + 9.2 log(N1)60

p′ = 0.47(N60)m Pa

Design Equation The Unified Design Equation (Chua et al. 2000)

'

viUultf

z

KKK

op

oU1

tan

41.0

223.0'

4.20 NP

Da

v

R

245tan

sin1

2

o

P

o

K

K

is determined as:

Probability of failure and reliability index (Withiam et al. 1998) g (R, Q) = R – Q

LRFD Concepts

Probability density functions for load and resistance

Probability of failure

Resistance Factors

12

= 3.0 Resistance Factor

Reese and O’Neill (1988) 0.55 in cohesionless soils

AASHTO (2007) 0.55 in cohesionless soils

Paikowsky (2004) 0.60 in IGM/weak rock

NUMERICAL MODELS

FULL SCALE MODEL REPRESENTATIVE VOLUME ELEMENT MODEL

RVE

Shaft

Shaft

A DEM MODEL OF THE RVE

TOP

LEFT

FRONT

• To minimize computational effort, the size of RVE should be just large enough to avoid any boundary effect

• Four different dimension ratios (X/Z = 4.7, 5.9, 6.9, and 9.1) are investigated The ratio between X and Z dimensions of the rectangular

box (RVE)

BOUNDARY EFFECT OF THE DIMENSIONS OF THE RVE

z

X

DIMENSION EFFECT OF X/Z

-10

0

10

20

30

40

50

60

0 5 10

% c

han

ge

in s

tres

s

Dimension Ratio (X/Z)

• The sample contains two kinds of particles • The dimensions of large ellipsoidal particles are

15:10:10 mm (Ra:Rb:Rc). • Ra, Rb, and Rc are the major and minor lengths of an

ellipsoid • The sizes of small particles are 12:10:10 mm

• The percentage of small particles by weight is 66%

Numerical Samples (RVE)

The friction coefficient is set to 0.1 to ease the rearrangement of particles during this phase

• Method A – Particles are generated randomly inside the RVE – The dimensions of the RVE are reduced in the Y and Z directions

until a desired void ratio (0.6 ei 0.8) is reached • Method B

– The initial dimensions of RVE are fixed according to the desired void ratio (0.6~0.8)

– Large particles (15:10:10 mm) are generated randomly – Small particles (6: 6: 6 mm) are generated randomly – No particle is in contact – The initial dimensions of RVE are different according to the

desired void ratio – The sides of small particles increase until the dimensions are

12:10:10 mm

Preparation of Numerical Samples

• Initial samples created by Methods A and B are compressed 1-D along the z-direction

• No lateral displacement is allowed to simulate the 1-D compression.

• Before the compression, the friction coefficient is set to 0.5 and the system is allowed to reach equilibrium

• Samples are compressed vertically to various vertical stresses

Preparation of Numerical Samples

Vertical Stress = 50 kPa

Effect of Sample Preparation

Method A Method B

Void Ratio Ko Void Ratio Ko

0.664 0.751 0.700 0.662

0.661 0.711 0.670 0.641

0.642 0.644 0.646 0.58

0.619 0.550 0.619 0.489

0.599 0.540 0.599 0.460

Vertical Stress = 50 kPa

Effect of Sample Preparation Coefficient of Earth Pressure at rest, Ko (= x/z)

• A vertical displacement is applied on the front surface to model the downward movement of a shaft

• The simulation is stopped when the peak shear stress on the front surface is observed

• is the ratio between shear stress and the initial vertical stress

• The shaft movement is defined as the ratio between the front face (shaft) movement and the vertical dimension of the system (Z)

Simulations of Side Resistance

Simulations of Side Resistance

Effect of Sample Preparation Side Resistance

Vertical Stress = 50 kPa

Ko versus Vertical Stress (Method A)

Ko = 34.693e2 - 40.988e + 12.598

• An increase of vertical stress on the top and bottom surfaces is observed

• The vertical stress on the bottom surface increases more than that of the top surface

• The magnitude of increase is a function of void ratio of the sample

• Greater amount of increase is observed for denser samples

• Normal stress also increases on the front plane (the interface between the particles and the shaft) but not on the back plane

• The normal stress on the back plane does not change.

Results of Simulations of Side Resistance

Development of Side Resistance with Shaft Movement

50 kPa

100 kPa

200 kPa

400 kPa

e = 0.656~0.664

Side resistance, Void Ratio, and Vertical Stress

50 kPa

100 kPa

200 kPa

400 kPa

bae

1

Parameters a and b versus vertical stress

bae

1

a

b

Hyperbolic Curve Fitting and Observed Data

Characteristics of These Design Equations

Unified method

NHI

100 kPa

200 kPa

400 kPa

Characteristics of DEM simulations

50 kPa

100 kPa

200 kPa

400 kPa

bae

1

Comparison between Design Equations and DEM Data

= 30o = 36o = 42o

e

United Design Equation

O’Neill and Reese Design Equation

Comparison with A Field Test • A static compression load test of a drilled shaft has been

conducted near San Juan Pueblo, New Mexico • The length and diameter of the shaft are 13.5m and 0.75 m • Due to caving of the near surface site soils, about upper 5.4m of

each shaft was encased in 0.8m outside diameter permanent steel casing

• The excavation of the shaft was performed using the bentonite slurry assisted construction. Concrete was delivered into the shaft hole using a tremie pipe.

INSTRUMENTATION • Load and displacement measurements for the butt • Telltales extending to the shaft tip, and • Measurements of a total of 16 strain gages located at various

depths.

Boring Log Summary (1ft=0.3048m)

Dep

th (

ft)

Blo

ws/

foot

REMARKS

VISUAL

CLASSIFICATION

Dep

th (

ft)

Blo

ws/

foot

REMARKS

VISUAL

CLASSIFICATION

5'

10'

15'

20'

25'

30'

35'

40'

45'

50'

55'

60'

65'

70'

75'

80'

85'

90'

33

50/5"

50/3"

50/5"

50/4"

50/6"

50/4"

50/5"

50/3"

50/5"

50/6"

PROJECT: NM 74 Over Rio Grande LOG OF TEST BORING NO. 2

Dense to

very

dense

Very dense

Hard

Hard

Loose to

medium @

45'

GRAVEL, Poorly

graded, occasional

cobble, nonplastic,

gray.

SAND, predominantly

fine to medium, trace

to some silt,

nonplastic, light gray.

SAND, predominantly

fine to medium, trace

to some silt,

nonplastic, tan.

SILTY SAND, fine,

nonplastic, tan.

SILTY SAND,

predominantly fine,

nonplastic, light

brown.

50/6"50/5"

50/3"

11

WATER TABLE

@ 6.5 FEET

Dep

th (

ft)

Blo

ws/

foot

REMARKS

VISUAL

CLASSIFICATION

Dep

th (

ft)

Blo

ws/

foot

REMARKS

VISUAL

CLASSIFICATION

5'

10'

15'

20'

25'

30'

35'

40'

45'

50'

55'

60'

65'

70'

75'

80'

85'

90'

33

50/5"

50/3"

50/5"

50/4"

50/6"

50/4"

50/5"

50/3"

50/5"

50/6"

PROJECT: NM 74 Over Rio Grande LOG OF TEST BORING NO. 2

Dense to

very

dense

Very dense

Hard

Hard

Loose to

medium @

45'

GRAVEL, Poorly

graded, occasional

cobble, nonplastic,

gray.

SAND, predominantly

fine to medium, trace

to some silt,

nonplastic, light gray.

SAND, predominantly

fine to medium, trace

to some silt,

nonplastic, tan.

SILTY SAND, fine,

nonplastic, tan.

SILTY SAND,

predominantly fine,

nonplastic, light

brown.

50/6"50/5"

50/3"

11

WATER TABLE

@ 6.5 FEET

Comparison among the Field Observation, Design equations, and DEM result

Unified

Equation

NHI

FHWA

Field Data

DEM

simulation

Bottom of

casing

A linear relationship between Relative density (Dr) and e c and d are functions of vertical stress and can also be approximated by second order polynomials as parameters a and b for ’v 200 kPa When ’v > 200 kPa, c and d will be constant just as a and b

Characteristics of (1/2)

RDdc

1

bae

1

For ’v 200 kPa Constants c1 c2 c3 and d1 are independent of vertical stress Skempton (1986) suggested the following relationship between standard

penetration resistance (N ) and DR: Where f and g are constants will be functions of ’v and N

A general form of the new design equation is identified

Characteristics of (2/2)

) 1)((

1

132

2

1 Rvv Ddccc

v

Rgf

ND

2

• The side resistance of drilled shafts has been simulated numerically using the DEM

• The DEM result shows that the relationship between and void ratio (relative density) is quite complicated than the current design equations

• is a function of void ratio (relative density) and vertical stress.

• Some design equations include the parameter Ko.

However, the numerical result do not show any direct relationship between Ko and .

In the field Ko is related to void ratio and the state of stress.

CONCLUSIONS

• Differences between DEM simulations and current design equations have been observed

• Void ratio is very important on side resistance at shallow depth but not at greater depth

• O’Neill and Reese design equation does not consider the effect of void ratio; the other two design equation do include void ratio, however, the trend is incorrect

• The new design equation should include a more complicated function of depth

• The general form of the new design equation is found • More DEM simulations are needed to develop the

parameters of the new design equation

CONCLUSIONS

This research is financially sponsored by the New Mexico Department of Transportation

Special thank to the Research Bureau Chief, Mr. Scott

McClure for his support and the sponsor Mr. Robert Meyers

ACKNOWLEDGMENT

Questions ?