Verification examples Earth pressure

1

multiPlas 5.1

Verification examples – earth pressure

© Dynardo GmbH, 2013 © Dynardo GmbH

Verification examples Earth pressure

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© Dynardo GmbH, 2013

Earth pressure – model

• load steps 1 – 3: excavation is filled with three layers of sand (EKILL and EALIVE) earth pressure at rest

• load step 4: rotation of left boundary around base point active earth pressure

• plane strain conditions (thickness 1 m)

• file: example_01.dat • parameters dimension and

order control type of elements:

dimension order element type

2 1 PLANE182

2 2 PLANE183

3 1 SOLID185

3 2 SOLID186

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multiPlas 5.1



Earth pressure – material properties of sand

• the following elastic parameters are given • density: ρ=1800 kg/m³ • constrained modulus: Es=40 GPa • coefficient of earth pressure at rest: k0=0.5

• calculation of isotropic material parameters:

• Poisson’s ratio: 𝜈 =𝑘0

1+𝑘0= 0.33

• shear modulus: 𝐺 =1−2𝜈

2(1−𝜈) 𝐸𝑠 = 10 𝐺𝑃𝑎

• Young’s modulus: 𝐸 = 2 1 + 𝜈 𝐺 = 26.7 𝐺𝑃𝑎 • shear parameters of sand:

• friction angle: φ=30° • cohesion: c=0 MPa

• nonlinear behavior of sand can be simulated with multiPlas: • law 1 – Mohr-Coulomb yield surface • law 40 – Drucker-Prager yield surface

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Earth pressure – multiPlas law 1

• combination of isotropic Mohr-Coulomb yield surface (shear failure) and isotropic Rankine yield surface (tensile failure)

• ideal plastic behavior • associated flow rule • law 1 parameters:

• initial/residual friction angle: 30°/30° • initial/residual cohesion: 1 Pa/1 Pa • dilatancy angle: 30°

• initial/residual tensile strength: 1 Pa/1 Pa • no joint sets

1 2 3 4 5 6 7 8 9 10

1-10 1 30° 1 Pa 15° 30° 1 Pa 1 Pa 1 Pa 0

11-20

21-30

31-40

41-50

51-60 0

61-70 1 1 1E-3 1E-20 10 4 0

71-80

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Earth pressure – multiPlas law 1 Results – PLANE182 – load steps 1 and 2

vertical displacements [m] load step 1 – installation of 1st sand layer

vertical displacements [m] load step 2 – installation of 2nd sand layer

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Earth pressure – multiPlas law 1 Results – PLANE182 – load step 3

vertical displacements [m] load step 3 – installation of 3rd sand layer

von Mises plastic strains end of load step 3 – installation of 3rd layer because of consistent elastic properties no

plastic strains at earth pressure at rest

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stresses [Pa] on left vertical boundary load step 3 – installation of 3rd sand layer

earth pressure coefficient end of load step 3 – installation of 3rd layer

because of consistent elastic properties the at rest earth pressure coefficient is 0.50

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vertical displacements [m] load step 4 – rotation of left boundary around

base point

von Mises plastic strains end of load step 4 – rotation of left boundary

around base point shear failure of sand

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plastic elements load step 4 – rotation of left boundary around

base point

plastic activity (last load increment) end of load step 4 – rotation of left boundary

around base point 0 – no activity

1 – Mohr-Coulomb yield surface activity

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stresses [Pa] on left vertical boundary load step 4 – rotation of left boundary around

base point

earth pressure coefficient end of load step 4 – rotation of left boundary

around base point active lateral earth pressure coefficient is

0.33 (corresponds to Mohr-Coulomb theory)

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Earth pressure – multiPlas law 40

• single Drucker-Prager yield surface • ideal plastic behavior • associated flow rule • law 40 parameters (Drucker_Prager cone inscribes Mohr-Coulomb yield surface):

• parameter β: 0.495 • parameter σ: 0 Pa • dilatancy factor: 1.0

1 2 3 4 5 6 7 8 9 10

1-10 40

11-20

21-30

31-40

41-50

51-60 0.495 0 Pa 1.0 0

61-70 1 1 1E-3 1E-20 10 4 0

71-80

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Earth pressure – multiPlas law 40 Results – PLANE182 – load steps 1 and 2

vertical displacements [m] load step 1 – installation of 1st sand layer

vertical displacements [m] load step 2 – installation of 2nd sand layer

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vertical displacements [m] load step 3 – installation of 3rd sand layer

von Mises plastic strains end of load step 3 – installation of 3rd layer because of consistent elastic properties no

plastic strains at earth pressure at rest

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stresses [Pa] on left vertical boundary load step 3 – installation of 3rd sand layer

earth pressure coefficient end of load step 3 – installation of 3rd layer

because of consistent elastic properties the at rest earth pressure coefficient is 0.50

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vertical displacements [m] load step 4 – rotation of left boundary around

base point

von Mises plastic strains end of load step 4 – rotation of left boundary

around base point shear failure of sand

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plastic elements load step 4 – rotation of left boundary around

base point

plastic activity (last load increment) end of load step 4 – rotation of left boundary

around base point 0 – no activity

1 – Mohr-Coulomb yield surface activity

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stresses [Pa] on left vertical boundary load step 4 – rotation of left boundary around

base point

earth pressure coefficient end of load step 4 – rotation of left boundary

around base point active lateral earth pressure coefficient is 0.32 (small deviation from Mohr-Coulomb

theory 0.33)

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Verification examples Earth pressure

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