Computer modeling of micropile systems with ZSoil

Andrzej TrutyAleksander Urbanski

Politechnika Krakowska

Kraków, 2014

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What is ZSoil ?

FEM software for solving 2D/3D static/dynamicsoil-structure interaction problems

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Main ZSoil capabilitiesStatics (short/long term) and transient dynamics forsingle and two-phase (partially saturated)media+structures

Stage construction and excavation analysis isallowed in the real time scale (including consolidationand/or creep effects)

Strong deformation discontinuities between thestructure-subsoil or structure-structure can beintroduced via Coulomb type interfaces

Small strain stiffness of soils can be represented by acomplex but easily calibrated nonlinear constitutivemodels (Hardening Soil-small (HSs) model forinstance)

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Why do we need FEM modeling of micropilesystems?

FEM models alow to analyze coupledmicropile-foundation-subsoil systems(rehabilitation of foundation of an existing building)

Serviceability and ultimate limit states can beanalyzed

FEM modeling helps to understand all interactionsbetween the micropile-foundation-subsoilcomponents

All kind of nonlinearities can be included (in micropileitself, subsoil, interfaces)

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Sources of nonlinearities inmicropile-subsoil-structure system

concrete

Steel elementsubsoil

micropile

Subsoil behaves in a nonlinear mannerInterface micropile-subsoil is probably the source ofstrongest nonlinearityIn some cases reinforcement-concrete interface canbe activatedConcrete can crack (if bending is activated)Other ?

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Sources of uncertainties in FEM models ofmicropile-subsoil-structure system

Subsoil: stress history (overconsolidation), initial porepressures, stiffness

1 Geostatic conditions (Ko in situ)2 Level of saturation3 Dilatancy (usually ψ =

16÷ 1

4φ′ in triaxial tests)

Micropile-subsoil interface: effect of micropileinstallation and dilatancy

1 During installation radial stresses increase locallynear the micropile (we add an axisymmetric stressfield into the general 3D state)→ K effect

2 Friction angle in the interface depends strongly on thetechnology

3 Strains are large (but only locally)

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Effective stress analysis in ZSoil (static case)Overall equilibrium: σtot

ij,j + fi = 0Effective stress principle σtot

ij = σ’ij + S p δij

Fluid flow continuity: S ·εkk + vF

k ,k − c·p = 0

Darcy velocity vFi = −kij kr (S)

(− pγF + z

), j

kr (S) function kr =(S − Sr )3

(1− Sr )3

S(p) (van Genuchten )

S(p) = Sr +1− Sr1 +

(α

pγF

)21/2

c(p) storage function c = c(p) = n(

SKF

+dSdp

)7 / 29

Effective stress analysis in ZSoil: possibledrivers

Quasi-undrained analysis→ short loading time, lowpermeability (in statics)

Steady state drained analysis→ long loading time

Transient case→ tracing pore pressure disipation inreal time

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Consequences of effective stress analysis

Parameters for soil constitutive model must beeffective→ c′, φ′

Undrained (su) or transient values of strengthparameters c, φ are naturally embeded in the theoryonce the consolidation driver is used and properelasto-plastic model is used

Cohesion results from suction pressure or effect ofcementation

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Soil constitutive models: M-C vs HSs

Elasto-plastic M-C model(frequently used in practice)

Ultimate limit states: YES

Serviceability limit states: NO (most often)

Elasto-plastic model HSs(since last few years quite often used in practise)

Ultimate limit states: YES

Serviceability limit states: YESTechnical report: R. Obrzud, A. Truty. THE HARDENING SOIL MODEL - APRACTICAL GUIDEBOOK Z Soil.PC 100701 report

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HSs model: 2 plastic mechanisms

f f

Double hardening model

Cap surfaces and failure cone (M-C) in principal stress space

p’

Isotropic hardening mechanism:cap yield surfaces p ydescribed with van Ekelen’s formula

Mohr-Coulombfailure surface

The Hardening Soil model with small strain stiffnessRafal Obrzud, GeoMod SA26.08.2013, Lausanne, Switzerland

- HS Standard

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HSs model: stiffness representation

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HSs model: calibration

(S)CPTU field test

(S)DMT field test

Triaxial test (CD) including shear wave velocitymeasurement as a calibration test for CPTU/DMTcorrelation formuli

CPTU/DMT serve us stress history parameter OCRand Ko in situ

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Micropile-subsoil interaction:fully conforming discretization (A)

Micropile (3D continuum)+interface

Subsoil

Resulting FE models are huge and extremely timeconsumingEach redesign of piles requires new mesh for wholesystem

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Fully conforming discretization: interfacetreatment

Interface thickness is zero

Contact stress computationσn,N+1 = kn gn,N+1

τN+1 = τN + ks ∆gs and |τN+1| ¬ σ′n tg(φ) + c′

kn and ks are penalty factors for rigid plastic interface

kn and ks can be related to the shear band thicknesst and its quasi-elastic stiffnesskn = E/t while ks = G/t

Rigid plastic interface leads to overstiffening of themicropile response

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Micropile-subsoil interaction:overlaid mesh approach (B)

Resulting FE models are smaller than for conformingmodelRelatively coarse mesh for subsoil is used whilemesh for micropile+interface+small part of subsoil isdense

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Micropile-subsoil interaction:micropiles as 1D members embedded in 3Dcontinuum (C)

Resulting FE models are smallSpecial interface must be implementedRedesign of micropile system is very easy

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Micropiles as 1D members embedded in 3Dcontinuum: interface treatment

Beam elementsMaster segment „m”

Master node of pile tipInterface „B”

Top pile node „T”

Plate/shell element „p”

3D continuum element „c”

Slave segment „s”

NB. Effect of micropile installation will be discussed later18 / 29

Interface micropile-subsoil in simplifiedapproach

τ=σn tan φ+c

ft=0, fc< fcult

xL

yL

zL

m1

m2s2

s1

segment mastersegment slave

In simplified approach there is no way to recover σn

from the interfaceHence we have to recover it from the adjacentcontinuum

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Interface micropile-subsoil in simplifiedapproach

Recovering σn from adjacent continuumxL

yL

zLR

R = SQRT (A/π)

ΔLiPi

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Effect of installation: K-pressure method

K-pressure method (PhD by Syawal Satibi, Stuttgart,2009)

In situ Ko state „excavation”  unloading is delayed

Add (K‐Ko) hAdd micropile/unload exc. forces/remove pressure

But how to define K value ?21 / 29

Effect of micropile installation

Micropile diameter is relatively small→ effect onincrease of radial stress due to installation islocalized in a relatively narrow zone

This effect can be analyzed in an analytical mannerusing known solutions for cavity expansion problem

In methods (A) and (B) we can use K-pressuremethod (PhD by Syawal Satibi, Stuttgart, 2009)

In method (C) K-pressure method is applicable butmesh size must be carefully choosen

Back analysis of load test may yield→ K value andinterface stiffness

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Effect of micropile installation in method (C):possible solution

Stress variation due to installation is neglected insubsoil

Equivalent interface friction angle tan (φ∗) has to beused to reproduce skin friction

This may lead to overestimation of micropilesettlements near the limit state

K-pressure is recommended (adding axisymmetricstress field)→ not available so far

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Effect of dilatancy in the interface zone

In methods (A) and (B) effect of dilatancy is present

In simplified approach (C) this effect is missing (sofar)

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An example: loading test on single micropileD = 18cm

‐0.025

‐0.02

‐0.015

‐0.01

‐0.005

00 100 200 300 400

Settlemen

t

Force [kN]

Simplified model

Experiment

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An example: micropile foundation system

3x3 and 5x5 micropile foundation system (D =20cm)

Micro-pile foundation system

3x3 and 5x3 D=0.2

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An example: micropile foundation systemComparison of:

3D FEM whith fully conformed mesh3D FEM with simplified ZSoil® method of pile modelling

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An example: micropile foundation systemComparison of displacements:3D FEM whith fully conformed mesh3D FEM with simplified ZSoil® method of pile modelling

UySimpl = 2.5mm

slighty stiffer (~15%) response

Uy=3mm s = 3 mm s = 2.5 mm (stiffer response)

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Conclusions

Proposed simplified approach is a very useful tool forsolving problems with large number ofmicropiles/piles

Standard discretization technique (A) is inefficient forcomplex 3D problems

Both approaches (A)/(B) and/or (C) require carefulcalibration of strength and stiffness parameters (byback analysis)

Combined standard design methods (for micropile)and numerical modeling of whole system seem to bethe most appropriate approach

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