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SCIENCE CHINA Technological Sciences, Volume 61 , Issue 7 : 1092-1106(2018) https://doi.org/10.1007/s11431-017-9269-7

A flexible various-scale approach for soil-structure interaction and its application in seismic damage analysis of the underground structure of nuclear power plants

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  • ReceivedDec 1, 2017
  • AcceptedApr 4, 2018
  • PublishedJun 11, 2018

Abstract

In simulations of geotechnical engineering, interface elements are versatile tools and are widely used in the modeling of the relative displacements between soils and structures. To consider the case of a local failure adjacent to a soil-structure interaction region, a partial mesh refinement should be performed. In this study, a three-dimensional (3D) interface element with an arbitrary number of nodes is developed as a new technique to reduce the complexity and difficulty of managing the various scales between soil and structure. An asymmetric number of nodes is permissible on the two sliding surfaces. In this manner, soil and structure can be discretized independently, and the various-scale model is established conveniently and rapidly. The accuracy of the proposed method is demonstrated through numerical examples. The various-scale approach is employed in an elasto-plastic seismic damage analysis of a buried concrete drainage culvert of a nuclear power plant. The results indicate that by applying the proposed method, the number of elements decreased by 72.5%, and the computational efficiency improved by 59% with little influence on accuracy. The proposed method is powerful for local damage evolution analyses of both soil and structure and possesses great practical significance and the potential for further application, especially for nonlinear analysis of large-scale geotechnical engineering.


Acknowledgment

This work was supported by the National Key R&D Program of China (Grant No. 2017YFC0404900), the National Natural Science Foundation of China (Grant Nos. 51779034, 51678113) and the Fundamental Research Funds for the Central Universities (Grant No. DUT17ZD219).


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  • Figure 1

    (Color online) The developed 3D interface element. (a) Typical 3D interface element; (b) numerical process.

  • Figure 2

    (Color online) Sub-element.

  • Figure 3

    (Color online) Modeling process.

  • Figure 4

    (Color online) Interface test for linear elastic and elasto-plastic behavior.

  • Figure 5

    (Color online) Relationship of the shear displacement and the shear stress of the interface.

  • Figure 6

    (Color online) Models of the footing penetrating into the soil. (a) Fine mesh (traditional 8-nodes interface element); (b) typical mesh with traditional 8-nodes interface element (case V); and (c) typical mesh with the proposed interface element (case 5).

  • Figure 7

    (Color online) The relationship between the vertical load and the displacement of the measuring point.

  • Figure 8

    (Color online) The relationship between the maximum differences and the ratio of footing element volume/number of sub-elements.

  • Figure 9

    (Color online) Models of the footing sliding example. (a) Fine mesh (traditional 8-nodes interface element); (b) typical mesh with traditional 8-nodes interface element (case IV); (c) typical mesh with proposed interface element (case 5).

  • Figure 10

    (Color online) The relationship between the horizontal load and the displacement of the load point.

  • Figure 11

    (Color online) The relationship between the maximum differences and the ratio of soil element (under footing) volume/number of sub-elements.

  • Figure 12

    (Color online) Model of the buried drainage culvert.

  • Figure 13

    (Color online) The acceleration times of the seismic waves. (a) Horizontal direction (perpendicular to the flow direction); (b) horizontal direction (along the flow direction); and (c) vertical direction.

  • Figure 14

    (Color online) Acceleration amplification response spectrum for 5% damping. (a) Horizontal direction; (b) vertical direction

  • Figure 15

    (Color online) The principal stresses of the central segment of the culvert before the earthquake.

  • Figure 16

    (Color online) Time history of the relative displacement between the top and bottom plates.

  • Figure 17

    (Color online) The occurrence and development of tensile damage to the culvert.

  • Figure 18

    (Color online) The maximum principal stresses on the culvert during the earthquake.

  • Figure 19

    (Color online) The principal stresses on the culvert after the earthquake.

  • Table 1   Results of the interface test with the linear elastic material

    Node

    δx (10–2 m)

    δy (10–4 m)

    5

    0.9999999

    −1.0000000

    6

    1.0000000

    −1.0000000

    7

    1.0000000

    −1.0000000

    8

    1.0000000

    −1.0000000

    9

    1.0000000

    −1.0000000

    10

    0.9999999

    −1.0000000

    11

    0.9999999

    −1.0000000

    12

    1.0000000

    −1.0000000

    13

    1.0000000

    −1.0000000

  • Table 2   Parameters of the generalized plastic interface model

    Elastic modulus

    Critical state

    Particle breakage

    Ds0 (kPa)

    Dn0 (kPa)

    Mc

    eτ0

    λ

    A (kPa0.5)

    b

    c

    1000

    1500

    0.88

    0.4

    0.091

    224

    0.06

    3.0

    Plastic direction

    Plastic modulus

    Loading direction

    α

    rd

    k

    H0 (kPa)

    fh

    km

    Mf

    0.65

    0.2

    0.5

    8500

    2

    0.6

    0.65

  • Table 3   Detailed information for each case in the simulation of footing penetrating into soil

    Interface element

    Case

    Number of interface elements

    Size of footingelements (m) (x´z)

    Size of soilelements (m) (x´z)

    Maximum difference (%)

    Point A

    Point B

    8-node interface element

    Fine mesh

    576

    0.05´0.05

    0.05´0.05

    8-node interface element

    I

    144

    0.1´0.1

    0.1´0.1

    1.83

    1.70

    II

    96

    0.1´0.15

    0.1´0.15

    2.82

    2.74

    III

    72

    0.1´0.2

    0.1´0.2

    3.74

    3.84

    IV

    64

    0.15´0.15

    0.15´0.15

    3.76

    3.78

    V

    48

    0.15´0.2

    0.15´0.2

    4.74

    4.86

    VI

    36

    0.2´0.2

    0.2´0.2

    5.63

    5.94

    Proposed interface element

    1

    144

    0.05´0.05

    0.1´0.1

    0.06

    0.02

    2

    96

    0.1´0.15

    0.08

    0.04

    3

    72

    0.1´0.2

    0.09

    0.06

    4

    64

    0.15´0.15

    0.08

    0.06

    5

    48

    0.15´0.2

    0.09

    0.09

    6

    36

    0.2´0.2

    0.10

    0.11

  • Table 4   Detailed information for each case in the simulation of footing sliding

    Interface element

    Case

    Number of interfaceelements

    Size of footing elements(m) (x´z)

    Size of soil elements(m) (x´z)

    Maximum

    Error (%)

    8-node interface element

    Fine mesh

    576

    0.05´0.05

    0.05´0.05

    8-node

    interface

    element

    I

    144

    0.1´0.1

    0.1´0.1

    10.1

    II

    96

    0.1´0.15

    0.1´0.15

    14.7

    III

    72

    0.1´0.2

    0.1´0.2

    17.0

    IV

    64

    0.15´0.15

    0.15´0.15

    17.5

    V

    48

    0.15´0.2

    0.15´0.2

    21.9

    VI

    36

    0.2´0.2

    0.2´0.2

    23.3

    Proposed

    interface

    element

    1

    144

    0.05´0.05

    0.1´0.1

    0.97

    2

    96

    0.1´0.15

    1.28

    3

    72

    0.1´0.2

    1.64

    4

    64

    0.15´0.15

    1.78

    5

    48

    0.15´0.2

    2.07

    6

    36

    0.2´0.2

    2.73

  • Table 5   Detailed information for each case of finite element model of buried drainage culvert

    Case

    Interface element

    Number of foundation elements

    Number of culvertelements

    Normalized computational time

    Static

    Seismic

    I

    proposed interface element

    261660

    134820

    0.60

    0.41

    II

    8-nodes interface element

    1309640

    134820

    1.00

    1.00

  • Table 6   Parameters for the concrete plastic damage model for the culvert

    ρ (kg/m3)

    E (GPa)

    ν

    ft (MPa)

    fc (MPa)

    lc (m)

    Gt (N m–1)

    2450

    31

    0.167

    3.48

    27.6

    0.4

    325

  • Table 7   Parameters for the generalized plasticity model for the foundation

    Elastic modulus

    Plastic and loading direction

    G0

    K0

    ms

    mv

    Mg

    Mf

    αf

    αg

    800

    1000

    0.8

    0.8

    1.72

    0.7

    0.411

    0.3

    Plastic modulus

    ml

    mu

    rd

    γDM

    γu

    β0

    β1

    H0

    HU0

    0.14

    0.5

    20

    30

    5

    60

    0.0525

    2450

    1600

    All the parameters are dimensionless

  • Table 8   Parameters of ideal elasto-plastic interface model

    k1

    k2 (kPa/m)

    n

    φ (°)

    300

    1´107

    0.8

    41.5

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