Soil penetration analyses with the Material Point Method

Lars Beuth, Deltares

11 June 2015 Deltares

Contents

1. Introduction to the Material Point Method (MPM)

2. Cone Penetration Testing (CPT)

3. Pile installation

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Introduction to the MPM

3

Initial position of material points

Final position of material points

MPM

deformed mesh at true scale

MPM is extension of UL-FEM, better suited for modeling large deformation processes.

Updated Lagrangian FEM (UL-FEM)

Introduction to the MPM

Initial configuration Calculation step ≅ UL-FEM

Resetting the mesh

Fully 3D code but allows for plane strain and axisymmetric analyses when considering a thin slice or wedge-shaped geometry.

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Equilibrium equations solved at nodes for nodal displacement increments.

external internal= −M u F F

nodal acceleration vector

mass matrix

external load vector

internal force vector

Introduction to the MPM

5

Dynamic explicit approach

Solution advanced in time steps.

stiffness matrix

external internal∆ = −K u F F

incremental displacement vector

Introduction to the MPM

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Quasi-static implicit approach

Quasi-static problems : Slow loading / deformation processes in which inertia forces can be neglected, generally stretching over longer periods of time of hours, days, years, e.g. creep processes.

Quasi-static implicit approach : Significantly shorter computation times than with dynamic explicit approach, easier to use. Advancement of simulation in load steps.

Introduction to the MPM

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Undrained conditions ⇒ “Effective stress” analyses Generation of excess pore pressures estimated but dissipation not considered

Partially drained conditions ⇒ 2-phase formulation Generation as well as dissipation of excess pore pressures with time

Modeling of saturated soil

Unique strength of the developed MPM : Simulation of dynamic and quasi-static soil-structure interaction problems considering soil-water interaction, e.g. consolidation, groundwater flow, erosion / sedimentation.

2. Cone Penetration Testing

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1. Considering partially drained conditions (Ceccato, 2015) 2. Considering undrained clay (Beuth, 2012)

Cone Penetration Testing (CPT)

Measurement of

• tip resistance qc

• sleeve friction

• pore water pressure

⇒ MPM analyses : better understanding of (large deformation) processes and thereby more accurate estimates of soil properties such as permeability, strength and stiffness for geotechnical analyses.

Cone penetration at low constant velocity

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CPT

A wedge of the axisymmetric problem is considered

p

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CPT

1. Considering partially drained conditions

excess pore pressures

When evaluating CPT measurements, soil is assumed either drained or undrained.

In case of e.g. silty soils, dissipation of excess pore pressures has considerable influence on CPT measurements, e.g. qc, and thus on soil parameter estimation.

Ceccato performed 2-phase CPT analyses taking into account dissipation of pore pressures during penetration.

CPT

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k = 10-5 m/s

k = 10-6 m/s

1. Considering partially drained conditions

Ceccato (2015)

Tip stress at steady-state corresponds to tip resistance qc

CPT

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1. Considering partially drained conditions

Ceccato (2015)

Permeability k [m/s]

Good agreement with reference solution.

CPT analyses with MPM allow refinement of soil parameter estimates from CPT measurements, e.g. through improvement of published empirical correlations.

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Numerical analyses of CPT in undrained clay using an advanced soil model to relate qc to undrained shear strength su.

CPT

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2. Considering undrained clay

Undrained shear strength su no unique soil property but depends on effective mean stress and type of loading : triaxial compression, triaxial extension, simple shear

Hansen & Clough, 1980

Stress path dependency due to anisotropic strength of clay.

Anisotropic Undrained Clay (AUC) takes into account :

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CPT

2. Considering undrained clay

Mc f = 0

q

p’ p’p,0

α0

2 su, extension

2 su, compression

• Stress path dependency of undrained shear strength

• Anisotropic strength of natural clay

• Shear-induced generation of excess pore pressures

Much more accurate than e.g. Tresca model which considers su stress-path independent, yet easy to use. Only few soil parameters : ϕ’cs OCR E’ ν’ As yet, only for normally-consolidated clay (OCR = 1)

10 cone diameters penetration. Regions of triaxial compression are colored blue.

CPT

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AUC Tresca

Regions of triaxial compression

2. Considering undrained clay

Effective mean stresses

AUC Tresca

AUC model : su,compression = 3 kPa, su,extension = 1.2 kPa, su,simple shear = 2.2 kPa (OCR = 1)

For comparison, Tresca model : su,compression = su,extension = su,simple shear = 4 kPa

CPT

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Tresca : qc / su,ss = 12.5 AUC : qc / su,ss = 11.6

Tresca su,compression = su,extension = su,simple shear = 4 kPa

AUC su,compression = 3 kPa, su,extension = 1.2 kPa, su,simple shear = 2.2 kPa

2. Considering undrained clay

Good agreement with previous studies, qc / su,ss = 12.5 (Lu et al, 2004)

CPT

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2. Considering undrained clay – Why CPT analyses using AUC model ?

Vermeer, Jassim, Hamad (2010) Need and performance of a new undrained clay model

Bjerrum, 1973

𝑠𝑢 =𝑞𝑐 − 𝜎0𝑁𝑐

σ0 … overburden stress

All AUC parameters (strength / stiffness) can be estimated easily except OCR. How estimate OCR ?

su is well correlated to qc via published cone factors Nc :

⇒ CPT analyses using AUC model to relate for given soil parameters of strength and stiffness qc

to su as a function of OCR.

⇒ Simple more reliable analyses of geotechnical problems involving undrained clay using AUC

model.

3. Pile installation

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Nguyen (2013)

Pile jacking in dry sand (centrifuge tests)

Pile installation

Numerical study allows to take into account installation effects (soil densification, evolving stresses) in numerical analyses involving wished-in-place pile foundations.

Loose sand Medium dense sand 0.62

0.65

0.68

0.72

0.75

0.78

0.81

0.84

Void ratio e

NS-VIP project : „Supplementary“ to VIBRO project

Pile installation

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3 piles installed by impact driving, 3 piles by vibratory driving. Lateral load tests performed on all piles to investigate whether both techniques render same lateral capacity. ⇒ vibratory driving up to full installation depth ⇒ faster installation process, lower noise emission, increased safety, less predamage Extensive soil testing before and after field test.

Regulatory bodies informed

Pile installation

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NS-VIP project : „Supplementary“ to VIBRO project

Carbon Trust, UK

1. Numerical simulation of

• vibratory and impact driven pile installation • subsequent lateral load tests

2. Validation of simulations with field test results

⇒ 3. Generalization of study to different initial soil densities and pile diameters Support by FLOW consortium, in close cooperation with VIBRO project specifically RWE Innogy. Agreed cooperation with IHC Merwede.

NS-VIP project

Pile installation

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Numerical analyses require consideration of : • large deformations • complex nonlinear material behavior : dependency of stiffness, strength and

dilation on density and stress (Hypoplasticity) • 2-phase material behavior • dynamic and cyclic loading under high frequencies • 3D as lateral load test is non-symmetric • liquefaction at zero effective stress

NS-VIP project

Pile installation

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Galavi, Zuada Coelho, Chmelnizkij, Beuth

contact friction coefficient µ = 0.3

One set of material parameters for all 4-5 sand layers found at the site. For each sand layer only input of initial density is adjusted.

Hypoplastic soil model parameters for pile driving simulations estimated on basis of field and laboratory measurements. CPT analyses used to validate parameters with available CPT field measurements.

NS-VIP project

Pile installation

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F(t)

NS-VIP project

Pile installation

Assessment of simplifications and optimizations with regard to computation time : geometry, mesh refinement and mesh dimensions, initial and final penetration depth of analyses Lateral load test analyses : change of geometry, switch from partially drained / undrained analyses to drained analyses, switch from dynamic to quasi-static MPM

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F