Numerical Simulation of Pipe-Soil Interaction by zzt18091

VIEWS: 248 PAGES: 19

									  Numerical Simulation of Pipe-Soil Interaction

                  Diana Lorena Castaño Acevedo

                 Grupo de Investigación en Geotecnía
            Universidad de Los Andes – Bogotá, Colombia
Centro de Estudios Interdiciplinarios Básicos y Aplicados en Complejidad
                                 -CeiBa-

                              Abril 3 de 2009


                   Diana Lorena Castaño A. Buenos Aires                    1 / 19
Introduction
Considerations – Spangler, Marston and FEM

                                                                       • Differs between kinds of Pipes
                                                                         (Flexible / Rigid)
                                                                       • Soil is considered to have an Elastic
                                                                         behavior
                                                                       • Fill is considered to have an Elastic
                                                                         Behavior
                                                                       • Only properties of a vertical column
                                                                         of soil/fill affect results




• Model has an exact geometry, which includes trench
  angle (b)
• Different constitutive models can be used in natural soil
• Different constitutive models can be used in fill
• It takes into account the different friction coefficients
  that exist between materials.
                                                                                                        2 / 65




                                Diana Lorena Castaño A. Buenos Aires                                             2 / 19
Outline



          1. Traditional Design Methods.
          2. Constitutive Methods
          3. FEM Analysis
          4. Results
          5. Numerical Example – Emisario Cartagena
          6. Preliminary Design Abaqus




                                                               3 / 65




                        Diana Lorena Castaño A. Buenos Aires            3 / 19
Traditional Design Methods
Flexible Pipes – Spangler Theory
           In flexible pipes, pipe material stiffness is negligible in
           comparison with soil stiffness.
                           Δχ =
                                    DL KWc r 3      Δy   (DLWc + Wl )Wc
                                  EI + 0,061E´r 3      =
                                                    D 149 PS + 61000 M s
           Where,
           DL         Deflection Factor
           K          Foundation Constant
           Wl         Live load at top of pipe (N/m2)
           WC         Dead load per pipe length
           r          Pipe radius
           E          Youngs Modulus (Elasticity)
                                                                  π
           I          Inertia Modulus per pipe length       I=
                                                                  64
                                                                     (D   4
                                                                              −d4   )
           E´         Soil Modulus
           PS         Pipe stiffness (kPa)
           Ms         Constrained soil modulus (MPa)
           D          Outer pipe diameter                                               4 / 65

           Δy         Vertical pipe diameter variation
           Δχ         Horizontal pipe diameter variation
                           Diana Lorena Castaño A. Buenos Aires                                  4 / 19
Traditional Design Methods
Rigid Pipes – Marston Theory


          In Rigid Pipes, pipe stiffness is much higher than soil stiffness.
          It is necessary to determinate if pipe resistance is enough to
          support applied load. Pipe takes the major portion of the loads.


                                                       ⎛        ′ ⎞
                                         (V + dV ) + ⎜ 2 Kμ V ⎟dh = V + γBd dh
                                                     ⎜        ⎟
                                                       ⎝   Bd     ⎠
                                                       ⎛        ′ ⎞
                                         (V + dV ) + ⎜ 2 Kμ V ⎟dh − V + γBd dh = 0
                                                     ⎜        ⎟
                                                       ⎝   Bd     ⎠
                                         dV ⎛        2 Kμ ′V          ⎞
                                           = ⎜ λBd −                  ⎟
                                         dh ⎜⎝         Bd             ⎟
                                                                      ⎠


                                                                                     5 / 65




                         Diana Lorena Castaño A. Buenos Aires                                 5 / 19
FEM Analysis
Constitutive Models - Elastic Model


          The general expression of Hooke's Law




                                                         ⎡1         1            ⎤
            σ ik = Ciklm ε lm = λδ ik δ lmε + 2μ ⎢ δ il δ km ε lm + δ imδ kl ε lm ⎥
                                                         ⎣2         2            ⎦
                                             lm



            σ = λtr [ε ]1 + 2μ ε
            σ = λe1 + 2με




                                                                                      6 / 65




                           Diana Lorena Castaño A. Buenos Aires                                6 / 19
FEM Analysis
Constitutive Models - Hypoplastic Model

          Hypoplasticity is a constitutive model developed for granular
          soils. It is constitutive equation should be written in an
          incremental way. Wollfersdorff equation (1996) improves
          mathematic formulation introducing four material constants that
          depend on stress and void relation and four other calibration
          constants that do not vary with material.


          Where,

          D         Strain rate

          fb        Barotropic’s factor

          fe        Pyknotropy factor
                                                                            7 / 65
          fd        Density factor


                          Diana Lorena Castaño A. Buenos Aires                       7 / 19
FEM Analysis
Constitutive Models - Hypoplastic vs Viscohypoplastic model

          1. Barotropic Factor is modified
          2. Pyknotropy and Density factor are removed.
          3. Void dependecy is introduced by OCR parameter




                                                                 8 / 65




                          Diana Lorena Castaño A. Buenos Aires            8 / 19
FEM Analysis
Geometry & Boundary Condition




                                                               9 / 65




                        Diana Lorena Castaño A. Buenos Aires            9 / 19
Results
Traditional design procedure




                                                                 10 / 65




                          Diana Lorena Castaño A. Buenos Aires        10 / 19
Results
FEM Results




   U2 Deformation for
   elastic natural soil
   material




                                                                 U2 Deformation for
                                                                 viscohypoplastic
                                                                 natural soil material

                                                                                 11 / 65




                          Diana Lorena Castaño A. Buenos Aires                        11 / 19
Results
FEM Vs Actual design




                                                              12 / 65




                       Diana Lorena Castaño A. Buenos Aires        12 / 19
Results
Bedding Base Displacement




                                                               13 / 65




                        Diana Lorena Castaño A. Buenos Aires        13 / 19
Results
Vertical Pipe Diameter Variation: Flexible pipe Vs Rigid pipe in FEM




                                                                       14 / 65




                           Diana Lorena Castaño A. Buenos Aires             14 / 19
Numerical Example 2 – Emisario Terrestre Cartagena
Geometry and materials




                                                                15 / 65




                         Diana Lorena Castaño A. Buenos Aires        15 / 19
Numerical Example 2 – Emisario Terrestre Cartagena
Measurements – Data Validation

                    AGUAS DE CARTAGENA S.A. E.S.P.
            ALC-06-BM-2006 - PROJECT EMISARIO TERRESTRE
                    Deflections in installation PRFV Pipes




                                                                16 / 65




                         Diana Lorena Castaño A. Buenos Aires        16 / 19
Numerical Example 2 – Emisario Terrestre Cartagena
Results




                                                       17 / 65




                Diana Lorena Castaño A. Buenos Aires        17 / 19
Preliminary Design Abaqus




                                                       18 / 65




                Diana Lorena Castaño A. Buenos Aires        18 / 19
Acknowledgment




                               Thanks !




                                                        19 / 65




                 Diana Lorena Castaño A. Buenos Aires        19 / 19

								
To top