Download - 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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multiPlas 5.1
Verification examples – earth pressure
© 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
Verification examples – earth pressure
© Dynardo GmbH, 2013
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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multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
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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multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
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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multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
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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multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
Earth pressure – multiPlas law 1 Results – PLANE182 – load step 3
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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multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
Earth pressure – multiPlas law 1 Results – PLANE182 – load step 4
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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9
multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
Earth pressure – multiPlas law 1 Results – PLANE182 – load step 4
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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multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
Earth pressure – multiPlas law 1 Results – PLANE182 – load step 4
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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multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
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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multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
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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multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
Earth pressure – multiPlas law 40 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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multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
Earth pressure – multiPlas law 40 Results – PLANE182 – load step 3
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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15
multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
Earth pressure – multiPlas law 40 Results – PLANE182 – load step 4
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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16
multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
Earth pressure – multiPlas law 40 Results – PLANE182 – load step 4
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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multiPlas 5.1
Verification examples – earth pressure
© Dynardo GmbH, 2013
Earth pressure – multiPlas law 40 Results – PLANE182 – load step 4
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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