Soil Model Parameters Identi cation via Back Analysis for ... … · Soil Model Parameters Identi cation via Back Analysis for Numerical Simulation of Shield Tunneling V. Zarev 1,

Soil Model Parameters Identification via Back Analysis forNumerical Simulation of Shield Tunneling

V. Zarev1, T. Schanz1, I. Dimov2 & M. Datcheva1,2

1Ruhr-Universitat Bochum, Germany2Bulgarian Academy of Sciences, Bulgaria

EURO:TUN 2013

Bochum, April 18, 2013

Veselin Zarev Soil Model Parameters Identification for Numerical Simulation of Shield Tunneling 1 / 22

Motivation − Model Parameters Identification (Constitutive and Geometrical)

Major difficulties in tunnel projects − estimation in a reliable way the mechanicaland spatial parameters of the subsoil

During the excavation − disagreement between the laboratory and field soil testdata (input parameters used in the numerical simulation), and the true responseduring the tunneling (measurements).

yy

xxx


Contents

1 3D Numerical Forward Model

2 Results of the Forward Simulation

3 Identification of the Soil Constitutive ParametersSensitivity AnalysisDirect Back Analysis

4 ResultsSensitivityBack Analysis

5 Summary


3D Numerical Forward ModelResults of the Forward Simulation

Identification of the Soil Constitutive ParametersResults

Summary

Typical Overview of a Closed Face Slurry Shield TBM

(1) Cutterhead Herrenknecht AG(2) Excavation chamber(3) Bulkhead(4) Slurry feed line(5) Air cushion(6) Wall(7) Segmental lining(8) Segmental erector




Summary

Main Dimensions of the FE-Model and Observation Points

Measured are the vertical displacements uz in nodes O12 and S12 during theexcavation of the shallow tunnel.

vector of model response small sub-model




Summary

Soil, Concrete Tunnel Lining, and TBM Model Parameters

Soil Constitutive ModelParameters Hardening Soil (HS) Modelϕ 35 [◦]ψ 5 [◦]c 10 [kN/m2]Eref

50 35 000 [kN/m2]Eref

oed 35 000 [kN/m2]Eref

ur 100 000 [kN/m2]pref 100 [kN/m2]m 0.7 [-]Rf 0.90 [-]νur 0.20 [-]γunsat 17 [kN/m3]γsat 20 [kN/m3]Rinter 0.60 [-]

Tunnel Lining TBMParameter Model: linear-elasticd 0.20 0.35 [m]E 30 000 210 000 [MPa]γ 24 38 [kN/m3]ν 0.10 0.30 [-]

Schanz, T., P.A. Vermeer and P.G. Bonnier, ′′The hardening soil model: Formulation andverification′′, Beyond 2000 in Computational Geotechnics - 10 Years of PLAXIS, 1999.




Summary

Calculation stages

Generating the initial stresses (K0 procedure in PLAXIS)

The steps which are modeled in a single excavation step are:

- excavation of the soil ahead of the TBM (deactivation of the finiteelements at that place with 1.50 m tunnel advance)

- applying a face support pressure at the tunnel face

- activation of the TBM shield, i.e. of the plate element (the next 1.50 m)

- applying the back-fill grouting pressure at the back of the TBM

- installing (activation) a new concrete lining ring with width of 1.50 m




Summary

Horizontal & Vertical Displacements by the Excavation of the ShallowTunnel (using the nominal values of the input parameters of the HS model)

Horizontal displacements Vertical displacementsin Y-direction: in Z-direction:

Figure: The observation points O12 (on the ground surface) and S12 (at the tunnel invert) areselected in the zones with significant vertical displacements (right image).

location of the observation points




Summary

Vertical Displacements in Nodes O12 and S12 during the Excavation of theShallow Tunnel (using the nominal values of the input parameters of the HS model)

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

0 15 30 45 60 75 90

0 10 20 30 40 50 60

u z[m

]

TBM advance [m]

Excavation stages [-]

heading face passing

O12

S12

Figure: Shown are also the used 2 × 13 = 26 observation points in the later direct back analysis,i.e. recorded are the vertical displacements in O12 and S12 after each 2nd excavation stage (i.e.

each 3rd meter) from excavation stage 6 to 30.




Summary

Sensitivity AnalysisDirect Back Analysis

Local Sensitivity Analysis (Step Size ∆xj = 10 %)

Scaled Sensitivities:

SSij =

(∂yi

∂xj

)xj (1)

yi denotes the ith observation (i.e. displacement)

xj denotes the jth input parameter

Finite difference approximation by the first-order forward-difference approximation:

y ′i (xj ) =∂yi

∂xj≈ ∆yi

∆xj=

yi (xj + ∆xj ) − yi (xj )

∆xj(2)

Composite Scaled Sensitivity for the jth parameter calculated for N observation points:

CSSj =

√√√√ 1

N

N∑i=1

(SSij

)2(3)

Vector of input parameters of the HS model: xxx = (ϕ, c,E ref50 ,E

refoed ,E

refur )

Vector of model response − vertical displacements in O12 and S12:

yyy = (uz (O12), uz (S12))location of the observation points




Summary




SSij =

(∂yi

∂xj

)xj (1)




y ′i (xj ) =∂yi

∂xj≈ ∆yi

∆xj=


∆xj(2)


CSSj =

√√√√ 1

N

N∑i=1

(SSij

)2(3)


refoed ,E

refur )






Summary




SSij =

(∂yi

∂xj

)xj (1)




y ′i (xj ) =∂yi

∂xj≈ ∆yi

∆xj=


∆xj(2)


CSSj =

√√√√ 1

N

N∑i=1

(SSij

)2(3)


refoed ,E

refur )






Summary


Concept of the Parameter Identification Procedure

Minimizing the discrepancy between the observations and the model responseThe Particle Swarm Optimizer (PSO) is used




Summary


Formulation of the Optimization Problem

Mean Squared Error:

f (xxx) =1

N

N∑i=1

(y calc

i (xxx) − ymeasi

)2(4)

xxx = (ϕ, c,E refoed ,E

refur ) − vector with the input parameters to be identified

y calci (xxx) − calculated data (i.e. vertical displacements) with parameter set xxx

ymeasi − measured data (synthetic)

N − total number of measurements = (points in the observation cross-section) ×(records during the excavation), i.e. 2 × 13 = 26 measurements in O12 and S12 aftereach 2nd excavation stage (i.e. each 3rd meter) from excavation stage 6 to 30.

Parameter Lower Bound Upper Bound1 ϕ 31 46 [◦]2 c 5 15 [kN/m2]

3 E refoed 17 000 53 000 [kN/m2]

4 E refur 48 000 150 000 [kN/m2]

Relations: ψ = ϕ− 30◦; E refoed = E ref

50 <1

2E ref

ur ; K nc0 = 1 − sinϕ




Summary


Particle Swarm Optimizer (PSO)

Stochastic, population-based optimization algorithm based on swarm intelligenceusing a population (swarm) of individuals (particles)Gradient-free, no rigorous convergence theory

Basic PSO algorithm (Kennedy and Eberhardt, 1995)

Updated particle velocity:

Vk (t) = ω(t)Vk (t − 1)︸︷︷︸momentum

+ c1r1

(X L

k − Xk (t − 1))

︸︷︷︸cognitive component

+ c2r2

(X G − Xk (t − 1)

)︸︷︷︸

social component

Updated particle position: Xk (t) = Xk (t − 1) + Vk (t)

k = 1, 2, 3, . . . Kp with Kp = number of particlesω(t) − inertia weight (Shi and Eberhart, 1997)

X Lk − local best position of the kth particle

X G − best position within the swarm

c1 and c2 − cognitive and social parameter

r1 and r2 − random numbers in the range [0;1]

t − current iteration step

V � � �� V� ��

� V��

� ��

��

��

��

� ��

PSO velocity and position update




Summary


Used PSO Modification - Approach with Linear Inertia Reduction(Shi and Eberhart, 1997)

Linearly decreased inertia weight at each iteration:

ω(t) = ωmax − ωmax − ωmin

Tmax(t − 1)

ωmax − initial inertia value

Tmax − maximum number of iterationst − current iteration step

(t − 1) − previous iteration step

ωmin − inertia weight at the last iteration

Large ω: favors global exploration by searchingnew areasSmall ω: favors local exploration

Used PSO parameters:

Np = 20

ωmax = 0.9

ωmin = 0.4

c1 = 0.50

c2 = 1.25

Tmax = 300

N.B. Almost all modifications of the PSO vary in some way the velocity-update rule.




Summary


Sub-model used in the Iterative Identification Procedure

Calc. time main model: more than 1 hour

Calc. time small sub-model: ca. 10 min

The small sub-model has the same perfor-mance as the main model, and it is usedto back-calculate the (synthetic) measure-ments by excavation of the shallow tunnel.

main model

-0.005

-0.004

-0.003

-0.002

-0.001

0

0.001

0 15 30 45 60 75 90

0 10 20 30 40 50 60

u z[m

]

TBM advance [m]



shield tail passing

HS, main modelHS, small model

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 15 30 45 60 75 90

0 10 20 30 40 50 60

u z[m

]

TBM advance [m]



shield tail passingHS, main modelHS, small model




Summary

SensitivityBack Analysis

Sensitivity in Observation Point O12 during the Excavation

0

0.002

0.004

0.006

0.008

0.01

0.012

0 15 30 45

0 10 20 30

Com

positeScaledSensitivities,CSSj

TBM advance [m]



12

18

x1 = c = 10 kN/m2

x2 = ϕ = 35◦

x3 = Erefur = 100000 kN/m2

x4 = Erefoed = 35000 kN/m2

x5 = Eref50 = 35000 kN/m2




Summary


Sensitivity in Observation Point S12 during the Excavation

0

0.002

0.004

0.006

0.008

0.01

0.012

0 15 30 45

0 10 20 30

Com


TBM advance [m]



12

18

x1 = c = 10 kN/m2

x2 = ϕ = 35◦

x3 = Erefur = 100000 kN/m2


x5 = Eref50 = 35000 kN/m2




Summary


Performance of the Optimization Solution

30

35

40

45

0 20 40 60 80 100 120

Param

eter

ϕ[◦]

Iterations

ϕmax = 1.3ϕ

ϕmin = 0.9ϕ

Final relative error = 0.91 %

Lower/Upper boundMin./Max. value

Exact value: ϕ = 35.0 ◦

15000

20000

25000

30000

35000

40000

45000

50000

55000

0 20 40 60 80 100 120

Param

eter

Eref

oed

[kN/m

2]

Iterations

Erefoed,max = 1.5Eref

oed

Erefoed,min = 0.5Eref

oed



Exact value: Erefoed = 35 MPa

4

6

8

10

12

14

16

0 20 40 60 80 100 120

Param

eter

c[kN/m

2]

Iterations

cmax = 1.5c

cmin = 0.5c



Exact value: c = 10 kN/m2

40000

60000

80000

100000

120000

140000

160000

0 20 40 60 80 100 120

Param

eter

Eref

ur

[kN/m

2]

Iterations

Erefur,max = 1.5Eref

oed

Erefur,min = 0.5Eref

oed



Exact value: Erefur = 100 MPa




Summary


Results − Local SA (Combined Sensitivity in Points O12 and S12; Assumed E ref50 = E ref

oed )

0

0.002

0.004

0.006

0.008

0.01

0.012

15 30 45

10 20 30

Com


TBM advance [m]



12

18

x1 = c = 10 kN/m2

x2 = ϕ = 35◦

x3 = Erefur = 100000 kN/m2


x5 = x4, i.e. Eref50 = Eref

oed

Largest final relative error (22.80 %) for c, because of the lowest sensitivity

Lowest final relative error (0.91 %) for ϕ, because of the largest sensitivity




Summary


Results − Local SA (Sensitivity in Points O12 and S12; Assumed E ref50 = E ref

oed )

in point O12: in point S12:

0

0.002

0.004

0.006

0.008

0.01

0.012

0 15 30 45

0 10 20 30

Com


TBM advance [m]



12

18

x1 = c = 10 kN/m2

x2 = ϕ = 35◦

x3 = Erefur = 100000 kN/m2



oed

0

0.002

0.004

0.006

0.008

0.01

0.012

0 15 30 45

0 10 20 30

Com


TBM advance [m]



12

18

x1 = c = 10 kN/m2

x2 = ϕ = 35◦

x3 = Erefur = 100000 kN/m2



oed




Summary

Summary

A numerical model is proposed to simulate a slurry shield mechanized tunnelingin a homogeneous ground domain employing a complex material model for thesoil (HS model)

It is suggested to use sub-modelling for creating an equivalent smaller model andreducing the calculation time required to solve the forward problem

Local Sensitivity analysis (LSA) is used to rank the constitutive model parametersregarding their importance in the model output

The performed back analysis of a synthetic displacement data in two observationspoints reveals the ability to identify the HS model parameters and it confirms theLSA ranking results




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Soil Model Parameters Identi cation via Back Analysis for ... … · Soil Model Parameters Identi cation via Back Analysis for Numerical Simulation of Shield Tunneling V. Zarev 1,