1

Numerical simulation software LinkFEA

Iris Summer Academy 2011

Mengxi WU

Institue of Mechanics,CASInstitue of Mechanics,CAS

04\09\201104\09\2011

(WP4)

Numerical simulation software LinkFEA

content What do we want to do Function of LinkFEA development of methods Application Conclusion and Expectation

1 What do we want to do

Design optimization and safety assessment of reservoir dams, tailing dams

Safety assessment risk management of dike against piping

slope sliding safety analysis under complicated situations

Main focus: numerical simulation method research and software developing

4

Dam

Seepage, deformation and stability analysis Water caused fracture at the first fill of a reservoir

5

Dike

Dike and piping Piping mouth

6

Slide range of a slope

Slope stability

Complicated Seepage situation (rain, water level rise and down of water reservoir )Slope Cut for construction

2 Function of LinkFEA

Finite element method software + safety assessment toolFocus

field simulation: seepage, stress and deformation, separately or coupled

safety assessment: structure, slope slidefield: hydraulic structure, tailing dam, slopeFunction: Pro-processor, simulation, and post-processor

Main Menu

Tree-shaped Menu

Draw AreaGeometry Toolbar

View Toolbar

Message Box

2.1 Main Interface

2.2 Pro-processor

Prepare for the FEM calculationGeometry, material parameter, calculation type and steps, load and boundary conditionMeshOutput contents

Independent Pro-processor function for 2-D Communication with CAD, pro-processor software

both for 2-D and 3-D

2.3 Computational modules Seepage analysis

variably saturated flow (including rain infiltration, evaporation)

Stress-deformation analysis geo-material and concrete structure

coupled analysis seepage and effective stress-deformation consolidation water caused structure fracture

2.4 post-processor

Visualization of results Field equal-contour lines and cloud map Variable vs. time

Structure strength safety slope slide safety

based on the FEM field effective stresses Find a critical surface with the minimum

safety by optimization techniques

3 development of methods

Innovative simulation method of variably saturated flow through porous media

Method of slope stability analysis

Seepage field can be get through the solution of Richards equation

r , ,

01 1

r , 2

02 0

[ ( )( ) ] ( ) ( )

( , t)

( ) ( )

( ,0) t = t

j ij i i

i i

ij j i i

i

k z K s s Q x

x x

k K z n q x

x

1. Relation of saturation and pore pressure （ VG equation ）：

2. Relation of relative seepage coefficient and saturation (Mualem equation)

(1 | | ) , 0( )( )

1 1, 0

n mr

er

s ss

s

1 1/m n

1/ 2 1/ 2r ( ) [1 (1 ) ]m m

e e ek s s s

( )s

Equation of underground flow

（ 1 ）

（ 2 ）

（ 3 ）

A function is adopted here to ensure the average value of be the chord value over the unsaturated pressure head domain or , which ensure the whole

calculation of the mass matrix be limited to within the un-saturation range, rather than involving saturation area both in temporal and spatial domain

1 0( )

0 0

时时

Innovative mass balance iteration technique

( )s

11 1

1 1

1 1

( ) ( ), ( ) ( ) | 0.01

( ) ( )( )

( ) ( 0.01), ( ) ( ) | 0.01

0.01

n

n

nn n n n

n n n n

nn n n n

s s

ss s

|

|

1[ ,min(0, )]n n 1[ ,min(0, )]n n

Piccard iteration method can be used directly

FEM equation with innovative iteration technique

1[ ( ) ( ) / ] ( ) ( ) / ( )n nIJ IJ n J I IJ n J IJ JK O t F O t K z ＝

IJ , ,K ( )= ( )e

I i r ij J je

N k K N d

IJe

O ( )= ( )e

I JN N s d

IF ( )e

n I IL eq N dL QN d

seepage analysis

Measured and Simulated water table positions at different time.

Measured and Simulated water table positions at different time.

2D rainfall infiltrationTransient seepage flow

2D transient drainage test

Mengxi Wu. “A finite-element algorithm for modeling variably saturated flows” . Journal of hydrology.2010

Inner seepage face simulation Procedure

Schematic map of the Procedure

10 m1k 12k > k

Mi

A

B

C

D

G

H

O

C'

D'

2 m

Zone 2Zone 1

EMj

Mk

M'k Free surface

Free surface

Inner seepage face

Interface elements

M'i

M'jFlux of added to M'jM j

While unconfined water flow from a fine-grained soils to a coarser soil, A zero pressure face (EO) may appear at the interface of the soils with water flows out of the saturated left side and goes to the unsaturated right side. EO is an inner seepage.The position should be determined and the flux should add to downstream nodes to keep mass balance.

0

0nq

Water table in Classic analysis

10 m

2 m

1k 12k =10 k

2.5 m 2.5 m

Oden & Kikuchi (1980)

Borja & Kishnani (1991)

Kazemzadeh-parsi & Daneshmand (2011)

Bardet & Tobita (2002)

E

A C

B D

F

O

G

H

saturated-only analysis varied saturated analysis

water table isnot accurate in classic saturated-only analysisConvergent problem exists in classic variably saturated analysis

2m

10m

1k

2.5m 2.5m

2k =10 k1

224 iterations225 iterations226 iterations

Zone 1 Zone 2

A

B

C

D

G

H

Validity and efficiency of the procedure

10 m

2 m

1k 12k =10 k

2.5 m 2.5 m

Zone 1 Zone 2

A

B

C

D

G

H

Pressure head contour

Iteration efficiency

or zero pressure line

Inner seepage face widely exists in zoned sections

15m

Zone 22k

10m

3.5m

13.5m 5m 10m

Drain

Zone 2

Kazemzadeh-Parsi & Daneshmand (2011)

2kZone 1

1k

2 1k =k

2 1k =4k

2 1k =10k

2 1k =100k

Inner seepage face procedure

Water table of a zoned earth dam Good iteration efficiency

Application: 3-d seepage analysis of water power stations .Paper: has sent to Journal of Hydrology for review

Under consideration:•different constitutive model of materials•complicated seepage case, Consolidation •soil strength reduction while saturation rise• coupled dynamic affect can be included

3.2 Slope stability analysis

Finite element stress-based method

Limit equilibrium method

(2) Search for the critical slip surface

Factor of safety function

1 2( , ,..., )nF F x x x

Circular sliding surface

Any shape sliding surface

Optimization techniquessteepest descent method, simplex method,…

min 1 2( , ,..., )nF F x x x Critical slip surface

(1) Calculate a safety factor for a specified slip surface

Enumeration method

Finite element stress-based method

Optimization method

4 Applications

Seepage, stress and deformation of several dams water caused fracture of dams in the first fill of

a reservoir Slope slide analysis, not yet

24

Seepage analysis of a hydropower station with a 320m high dam

Hinge dispose of Shuang-jiang-kou hydropower station

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Simulated water table of the powerstation(A seepage filler formed at the workshop)

reservoir

Underground workshop

downstream

合作

Some details

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pore water pressure around the workshopThe caves are seepage fillers

Stress-deformation analysis

2-D and 3-D stress-deformation coupled and uncoupledsoil-structure interaction

concrete cut-off wall

contact element

Changhe dam (240m high; in Sichuan prov. China)

Settlement displacements (m)

Major principal stress (MPa)

Seepage-Stress Coupled analysis

1479.4

1559

1671填 筑 高 程

-80 -40 0 40 80

Y(m )

1500

1550

1600

1650

Z(m

)

1479.4

1559

1671填 筑 高 程

-80 -40 0 40 80

Y(m )

1500

1550

1600

1650

Z(m

)

Comparison between uncoupled and coupled solution

Pore water pressure Excess pore water pressure

Conclusion and Expectation New methods in variably saturated flow are developed Software for field simulation of seepage, stress and

deformation works well in our practice. A friendly interfaces is still under developing. Function of slope stability analysis will be finished in a

month Fully coupled dynamic function capable of both pore

water pressure accumulation and dissipation effect will be developed, and safety under dynamic condition will be obtained.

Thank you for your attention !