brinkgreve technet 2018-2 - tu delft research portal · • software company, developing the plaxis...

Copyright Plaxis bv, 2018

New developments in PLAXIS:Material Point Method & Reliability Analysis

Dr. Ronald B.J. Brinkgreve, Plaxis bv / Delft University of Technology

(with help of Anita Laera, Markus Bürg)

Content

• Introduction

• Material Point Method (MPM)

– Performance improvements

– 3D modelling facilities

– Applications

• Reliability Analysis

– Sources of uncertainty

– Stochastic parameters

– Limit state function

– Calculations (FORM, Directional Sampling)

– Results

– Applications

• Conclusions

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Introduction

Who is Plaxis bv?

• Software company, developing the PLAXIS geo-engineering software

• Established in 1993 as a spin-off from TUDelft

• Headquarters in Delft (Delftechpark); offices in Singapore and US

• 60+ professionals in Research, Software Development, Quality,

Marketing, Sales and Services

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Introduction

What is PLAXIS?

• Geo-engineering software based on the Finite Element Method

• Stress, deformation, dynamics (earthquakes), stability, groundwater flow and

thermal analysis of soils, rocks and soil-structure interaction

• Applications: Foundations (onshore, offshore), excavations, embankments,

dams, slopes, tunnels, mining applications, …

• Key words: Efficient, robust, user-friendly, reliable

• Continuous improvements and new developments

• 19000+ licenses world-wide (2018)

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Introduction

Main topics of New Developments:

• Dynamic analysis, liquefaction (earthquakes)

• Structural design (in the ground), inter-operability, BIM

• Tunnels and rock modelling

• Monopile design for offshore wind turbines (MoDeTo)

• Large deformation analysis: Material Point Method (MPM)

• Reliability Analysis, Probabilistic Analysis (ProbAna)

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Material Point Method

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Numerical modelling of large deformations:

• Finite Element Method (FEM)

Limitations: distortion of mesh, flow of material, changing contact

� Material Point Method (MPM):

Material points can ‘flow’ through the calculation grid

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Challenges of MPM

Measures needed to overcome numerical difficulties, making MPM applicable for geo-engineering & design in practice:

• Points moving from one cell to another

• Dealing with empty cells

• Determining active boundaries

• Application of loads and boundary conditions

• Smoothing of stresses

• Contact formulation

• Stability and convergence of the calculation

• Efficient use of computer resources

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Soil MPM Soil FEM

Seamless connection of MPM and FEM

Division of geometry into different domains

• Soil MPM:

– Relaxation of mesh in Convective Phase

• Soil FEM:

– Using Updated Lagrange formulation

– Seamless connection to ‘relaxed’

MPM mesh

• Structure FEM

– Independent FEM mesh

• Contact boundaries

– Applied around structures to

‘sense’ contact with material points

– Cohesive-frictional properties

taken from soil in contact

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MPM applications

Typical geo-engineering applications involving large deformations:

• Slope failure, landslide

• Pile and anchor installation

• Spudcan penetration, punch-through, extraction

• Pipeline and cable movements

• Trenching, dredging

• Impact problems

• ...

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PLAXIS MPM: Pre-processing

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PLAXIS MPM: Pre-processing

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PLAXIS MPM: Post-processing

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MPM application: Spudcan penetration

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Reliability Analysis

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Reliability Analysis

Probability of failure against certain criteria

• Sources of uncertainty

• Stochastic parameters

• Limit State function

• Calculation methods

• Results

• Applications:

- Reliability of dykes

- Lifetime reliability of quay walls

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Sources of uncertainty

Aleatoric uncertainty (natural variation):

• E.g. variation of soil properties, weather conditions

Epistemic uncertainty

(lack of knowledge or inaccuracy):

• E.g. limitations of models, measurement errors

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Stochastic parameters

In Geo-engineering, stochastic parameters can be:

• Model parameters (soil, structures)

• Loads

• Water levels

• Geometric dimensions:

- Layer thickness

- Water depth

- Pile penetr. depth)

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Water levels:

• Stochastic distribution of water level (per segment)

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Correlation between parameters:

For example:

• Soil stiffness is related

to soil strength

Definition of correlation

matrix as column per

parameter

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Stochastic parameters > Stochastic results

Distribution of INPUT parameters leads to distribution of OUTPUT results

(INPUT and OUTPUT can be loads or resistances)

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Limit State Function

Limit State function (Z):

Z = R – S

R = measure of Resistance

S = measure of Load

Failure is defined as Z<0

Probability of failure =

overlapping area between

distributions of R and S

µ = mean value

σ = standard deviation

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Selecting parameters to define limit state criteria (based on result types):

Z = Criterion – Result

• Stresses or pore pressures in a point in the soil

• Displacements or strains in a point in the soil

• Anchor force

• Maximum displacement or force (as for example the bending moment) in a

plate or shell

• Shear or lateral traction in an embedded beam

• Global safety factor

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Selecting parameters to define limit state criteria (based on result types):

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Calculation methods

Monte-Carlo Method (MC)

• Random selection of stochastic parameters

• Requires very many calculations

First Order Reliability Method (FORM)

• Gradient type iterative calculation method (COBYLA or Abdo-Rackwitz)

• Highly reduced number of calculations

Directional Sampling (DS)

• Monte-Carlo type sampling method

• Smart selection of stochastic parameters (different strategies)

• Reduced number of calculations

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Calculation methods – FORM

Graphical representation of the FORM approach

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MPP = Most Probable Point or Design Point


Calculation methods

Comparing different

methods and

strategies

� Different accuracies

� Different number of

evaluations

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Results

Results

• Probability of Failure Pf

• Reliability Index β

• Design Point

(critical values of stochastic variables)

• Importance factors

• Histogram of results

• …

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Results

Results

• …

• Distribution of results

(Point cloud)

• Convergence:

• # iterations

• Errors

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Applications


Applications

Reliability analysis of quay walls

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(based on MSc thesis Herm-Jan Wolters, 2012)

Applications


Advantage of finite element method:

Different failure mechanisms can be considered simultaneously

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(courtesy of Alfred Roubos)


Applications


• Supporting research by Alfred Roubos (Havenbedrijf Rotterdam, TUDelft)

• Analysing reliability and rehabilitation of quay walls over their lifetime under

changing conditions (changing harbour depth, water levels, steel corrosion,

different loading conditions)

• Stochastic variables: soil parameters, layer thickness, retaining height, water

level differences, surface load, steel thickness (corrosion!)

• ‘Failure’ criteria: Global safety factor, bending moment in wall, steel stress

• Results also show influence of parameters on probability of failure

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Applications

Reliability of quay walls over time

• Including corrosion of combi-walls

• Probabilistic analysis can help and optimise the decision making

(maintenance, upgrading, demolish and rebuild)

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Applications

Reliability analysis of river dykes

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(based on MSc thesis Job Janssen, 2016)

Applications

Reliability analysis of river dykes

• Reinforcement by including retaining wall in the dyke

• Conventional design method leads to unrealistically heavy wall

(ULS design bending moment 2159 kNm/m vs. SLS design 247 kNm/m)

• Probabilistic analysis:

• Stochastic variables: soil parameters

• Results show that dyke is safe with less heavy (lower cost) structure

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Applications

Reliability analysis of river dykes - Results

21/02/2018 37(based on MSc thesis Job Janssen, 2016)

Conclusions

PLAXIS

• World-leading finite element software for geo-engineering applications

• Continuous new developments


• Large deformation analysis, material flow, installation effects, contact

• Making MPM applicable for geo-engineering & design

Reliability analysis (Probabilistic analysis)

• Parameters as stochastic variables, limit state criteria, probability of failure

• Applications (so far) in quay walls and river dykes

• Reliability analysis gives insight in failure causes and can help reducing cost

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Thank you

brinkgreve technet 2018-2 - tu delft research portal · • software company, developing the plaxis...

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