Dynamic Soil-Structure Interaction Analysis: Detecting the Reliability of Modelling the Piles as a Plate Element for a Multistory Building Resting on Deep Foundation

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Dynamic Soil-Structure Interaction Analysis: Detecting the Reliability of Modelling the Piles as a Plate Element for a Multistory Building Resting on Deep Foundation

Zeinab Zein1*, Lina Jaber2, Yehya Temsap

Department of Civil Engineering Beirut Arab University

Beirut, Lebanon

Abstract. Dynamic soil-structure interaction (SSI) is one of the main subjects that has attracted the attention of researchers in the recent decades. Numerous studies were interested in examining the seismic response of buildings supported on pile footings while including SSI. Most of these studies were simulating the problem by two dimensional models in the plane strain to overcome the usual difficulties encountered in 3D models. Commonly, piles were represented by plate elements of infinite length, disregarding the spacing between piles, and thus overestimating its stiffness. Recently, Plaxis a finite element software- has implemented a new feature known as the embedded pile row. Although this latter models the pile as a 2D structural element, it allows the definition of an out-of-plane spacing where the soil can flow around the piles upon keeping a continuous mesh. Many researchers have studied the reliability of the embedded row element and verified its validity. The objective of this paper is to define the limitations of employing the plate feature in soil- structure pile interaction analysis. This is achieved by comparing the behavior of the structure and the pile foundation using the plate feature to that of the embedded pile row. In this scope, a series of 2D finite element models consisting of multi- story buildings supported on pile footings are generated while varying the soil type, the earthquake frequency content, as well as the out-of-plane piles' spacing. This paper demonstrated that the building response with piles modeled as plate elements is just adequate when the surrounding soil is dense. Yet, regarding the pile response, the plate feature is unable to capture the real behavior for all soil types.

KeywordsPlaxis 2D; Embedded Pile Row; Plate Element; SSI; Dynamic Response

  1. INTRODUCTION

    Over the last few decades, several devastating earthquakes (Niigata earthquake (1964), the Kobe earthquake (1995), the Bhuj earthquake (2001), and the Sumatra earthquake (2004)) have caused severe damages to many structures especially for buildings resting on deep foundations. Therefore, the assessment of the behavior of the soil- pile foundation- structural system became crucial when subjected to earthquake dynamic loading.

    It is well acknowledged that the soil-structure interaction (SSI) influences the seismic response of buildings. Many types of researches were done to detect the influencing parameters that

    might affect the dynamic behavior of the building in a SSI problem. However, this problem is still under discussion due to the absence of real code provisions.

    While modeling the dynamic soil-pile-structure problem by employing the finite element method (FEM), most researchers tend to simulate the model using the two-dimensional approach to overcome the difficulties encountered in the three dimensional one (more time consumption, more memory usage). In a 2D model, it is common to design the pile as a plate element of infinite length in the out-of-plane direction, therefore overestimating the piles stiffness and disregarding the soil that is supposed to flow between the actual different piles.

    Plaxis a software that uses the finite element method FEM has implemented a new feature the embedded pile row that is able to simulate the 3D behavior of a pile while employing a 2D model. Several experimental and numerical studies were done to validate this new feature. The real case of the Alzey Bridge pile load test was modelled using the embedded pile row [1]. The comparison between the measurements and the Plaxis model showed that the embedded pile row predicts similar results of the pile capacity, and therefore, it is able to resemble the real pile behavior. For single piles, the behavior of embedded pile in compression and tension loading was validated upon comparing them with real tension tests and pile load test data [2]. For the group of piles, the embedded pile group was validated and showed a reasonable agreement with the measured data and clearly indicated the pile group effect [3-5].

    Sluis made a comparative study for the embedded pile row modeled as a 2D with that being modeled as a 3D [6]. The obtained results for the displacement of the embedded beam row in 2D showed a very good agreement with the 3D average soil displacement. The study showed that the choice of the optimal feature that can best simulate the piles behavior depends on the ratio of the center to center pile spacing to the diameter of the pile (Ls /D).

    The embedded pile row has been tested and validated as part of a thesis study in several states and loading conditions [7]. It was observed that the embedded pile was able to resemble the volume pile, and that it showed a good performance while being subjected to lateral soil movements caused by the construction of an embankment on soft soil. Kwaak [8] proved that the automatically generated interface stiffness factor (ISF) provides reasonable

    result for kinematic bending moment when compared to the calculation of D sheet piling program. He proved that the embedded pile row in a 2D model shows aptitudes for modelling dynamic pile behavior since it gives similar behavior as expected in 3D model when the interface stiffness factors and limiting lateral resistance are improved.

    The literature review has acknowledged the effectiveness of using the two-dimensional embedded pile row feature in simulating the real 3D pile behavior, as well as that the pile spacing plays a significant role in controlling the piles response. The aim of this study is therefore to detect the reliability of using the plate feature while modeling the piles in a seismic soil pile structure interaction problem. This is accomplished by conducting a dynamic soil pile structure analysis using the finite element method (FEM) for a multi-story building resting on a pile foundation. A series of 2D finite element models will be generated by employing Plaxis code to compare the behavior of the structure and the pile foundation using the plate feature to that of the embedded pile row. This is achieved while varying several parameters such as the soil type, earthquake input motion, and the pile spacing in the out of plane direction.

  2. PRINCIPLE OF EMBEDDED PILE ROW

    For modeling piled foundation, the Plaxis 2D Software provided the embedded pile row feature, in which the pile is assumed as slender beam element that can cross soil volume elements at any arbitrary location and orientation. This beam is connected to the soil by special interfaces, which describe the input parameters of the skin and foot resistance [9]. When the embedded pile row is applied while specifying its diameter, an equivalent elastic zone is created around the pile to simulate its behavior as a volume element. The interaction between the pile and the soil at the skin is modeled by means of the line-to-volume interface and is represented by springs with axial stiffness and lateral stiffness. In both directions, the springs force is limited by a maximum force (axial and lateral skin capacity). The soil and tip interaction is modeled as a point to volume interface and is represented by a spring with numerical stiffness (KF) and a slide. The springs force is limited by the input maximum base resistance [10].

    RS= ISFRS (Gsoil / Lspacing ) (1)

    N= ISFRN (Gsoil / Lspacing ) (2)

    KF= ISFKF (Gsoil * Req / Lspacing ) (3)

  3. THE MODEL DESCRIPTION

    A two-dimensional soil-pile-structure model is generated. It consists of a 24-story building of 12 m width and 3 m story height (H=72 m) supported on a group of pile foundation. A group of 10 piles of 0.5 m diameter and 10 m length, resting on a 50 m thick layer of homogeneous sandy soil with different stiffness were modeled once as a plate feature and twice as an embedded pile row, as shown in Fig. 2. The Mohr Coulomb constitutive model simulates the soil behavior. Three different earthquake input motions with different peak ground accelerations are applied at the bedrock level, located at the bottom of the soil domain (TABLE I). The study is done while varying also the pile spacing (Ls) for the embedded pile row model (Ls=1, Ls= 1.5, Ls=2 and Ls=2.5 m). The mechanical properties of the soil and the embedded pile row are shown in TABLE II and TABLE III.

    The soil unbounded medium is idealized as a finite domain by assigning viscous boundaries at the lateral boundaries and a compliant base at the bottom boundary [11]. The finite element method is adopted for the analysis where the size of the mesh element was chosen according to Kuhlemeyer and Lysmer [12]. It stated that the element mesh size should remain smaller than one-fifth to one-tenth the ratio of shear wave velocity and the highest frequency of the earthquake input motion. Rayleigh damping parameters are simulating the soil damping characteristics[13].

    Fig. 1 Two dimensional finite element model of building on top of

    soil domain

    Where,

    Gsoil: soil shear modulus RN: stiffness lateral direction Lspacing: out of plane spacing RS: stiffness axial direction Req: equivalent radius of the pile KF : stiffness lateral direction

    Interface stiffness factors (ISF) are calculated automatically by PLAXIS, based on the equations provided by Sluis [10]:

    ISFRS = 2.5 x (Lspacing/D)-0.75 (4)

    ISFRN = 2.5 x (Lspacing/D)-0.75 (5)

    ISFKF = 25 x (Lspacing/D)-0.75 (6)

    (a) (b)‌

    Fig. 2 Piles modelled as (a) Plate Element, and (b) Embedded Pile Row

    Earthquake Name

    Date

    Magnitude (Mw)

    Peak acceleration

    Max frequency (Hz)

    Duration (sec.)

    Loma Prieta

    1989

    5.7

    2.399 g

    2.893

    23.5

    Hollister

    1986

    5.45

    0.04353 g

    0.9

    40

    Coyote Lake

    1979

    5.74

    0.11663 g

    5.71

    27

    Earthquake Name

    Date

    Magnitude (Mw)

    Peak acceleration

    Max frequency (Hz)

    Duration (sec.)

    Loma Prieta

    1989

    5.7

    2.399 g

    2.893

    23.5

    Hollister

    1986

    5.45

    0.04353 g

    0.9

    40

    Coyote Lake

    1979

    5.74

    0.11663 g

    5.71

    27

    TABLE I CHARACTERISTICS OF EARTHQUAKES

    Parameter

    Symbol

    Unit

    Soil

    Identification

    Loose Sand

    Medium Sand

    Dense Sand

    Material Model

    Model

    Mohr-Coulomb

    Drainage Type

    Type

    Drained

    Soil Unit Weight saturated

    sat

    KN/m3

    17.5

    19.5

    20.5

    Soil Unit Weight unsaturated

    unsat

    KN/m3

    17.5

    19.5

    20.5

    Youngs Modulus

    E

    KN/m2

    44600

    323000

    5640000

    Shear Wave Velocity

    Vs

    m/s

    100

    250

    1000

    Poisson Ratio

    0.25

    0.3

    0.35

    Friction Angle

    Ø

    Degree

    29

    35

    40

    Dilatancy Angle

    Degree

    3

    5

    8

    Rayleigh Damping

    0.11

    0.2356

    0.6283

    Rayleigh Damping

    0.00159

    0.001273

    0.0006366

    Parameter

    Symbol

    Unit

    Soil

    Identification

    Loose Sand

    Medium Sand

    Dense Sand

    Material Model

    Model

    Mohr-Coulomb

    Drainage Type

    Type

    Drained

    Soil Unit Weight saturated

    sat

    KN/m3

    17.5

    19.5

    20.5

    Soil Unit Weight unsaturated

    unsat

    KN/m3

    17.5

    19.5

    20.5

    Youngs Modulus

    E

    KN/m2

    44600

    323000

    5640000

    Shear Wave Velocity

    Vs

    m/s

    100

    250

    1000

    Poisson Ratio

    0.25

    0.3

    0.35

    Friction Angle

    Ø

    Degree

    29

    35

    40

    Dilatancy Angle

    Degree

    3

    5

    8

    Rayleigh Damping

    0.11

    0.2356

    0.6283

    Rayleigh Damping

    0.00159

    0.001273

    0.0006366

    TABLE II MECHANICAL PROPERTIES OF MOHR COULOMB SOIL

    Parameter

    Symbol

    Unit

    Pile

    Material Model

    Elastic

    Youngs Modulus

    E

    KN/m2

    25.74E6

    Unit Weight

    KN/m3

    7.5

    Pile Type

    Predefined massive circular pile

    Diameter

    D

    M

    0.5

    Area

    A

    m2

    0.1963

    Moment of Inertia

    I

    m4

    3.068E-3

    Out of Plane center to center

    Lspacing

    M

    1

    1.5

    2

    2.5

    Axial Skin Resistance

    Soil Stiffness

    Loose Sand

    Medium Sand

    Dense Sand

    KN/m2

    72.5

    88.2

    170

    Tmax

    KN/m

    98.6

    120

    231

    Base Resistance

    Fmax

    KN

    Loose Sand

    Medium Sand

    Dense Sand

    7

    5.3

    6.3

    Interface Stiffness Factors

    Default values by Plaxis

    Axial Stiffness factor

    ISFRS

    1.487

    1.0967

    0.883

    0.7477

    Lateral Stiffness factor

    ISFRN

    1.487

    1.0967

    0.883

    0.7477

    Base Stiffness factor

    ISFKf

    14.87

    10.967

    8.83

    7.477

    Parameter

    Symbol

    Unit

    Pile

    Material Model

    Elastic

    Youngs Modulus

    E

    KN/m2

    25.74E6

    Unit Weight

    KN/m3

    7.5

    Pile Type

    Predefined massive circular pile

    Diameter

    D

    M

    0.5

    Area

    A

    m2

    0.1963

    Moment of Inertia

    I

    m4

    3.068E-3

    Out of Plane center to center

    Lspacing

    M

    1

    1.5

    2

    2.5

    Axial Skin Resistance

    Soil Stiffness

    Loose Sand

    Medium Sand

    Dense Sand

    KN/m2

    72.5

    88.2

    170

    Tmax

    KN/m

    98.6

    120

    231

    Base Resistance

    Fmax

    KN

    Loose Sand

    Medium Sand

    Dense Sand

    7

    5.3

    6.3

    Interface Stiffness Factors

    Default values by Plaxis

    Axial Stiffness factor

    ISFRS

    1.487

    1.0967

    0.883

    0.7477

    Lateral Stiffness factor

    ISFRN

    1.487

    1.0967

    0.883

    0.7477

    Base Stiffness factor

    ISFKf

    14.87

    10.967

    8.83

    7.477

    TABLE III MECHANICAL PROPERTIES OF EMBEDDED PILE ROW

  4. RESUTS AND DISCUSSIONS

    The model described in the previous section is generated while using the plate element feature in designing the piles. The responses of the building as well as the piles are therefore examined and then compared to the same model where piles are designed using the embedded pile row feature. This was achieved while varying the different parameters mentioned earlier. However, in order to ensure a fair comparison, the value of the shear stress in both models must be first unified. Accordingly, the value of the maximum shear stress of the pile resulting from the output of the plate model should be assigned as the Axial Skin Resistance (Tmax) in the defined material data set for the embedded pile row. Moreover, the value of the maximum axial force at the pile tip resulting from the output of the plate model should be designated as the Base Resistance of the embedded pile row.

    Regarding the piles response, the results will be evaluated in terms of the shear stresses, the horizontal displacements, and the maximum moment values along the piles height. As for the building response, the peak horizontal accelerations and displacements, as well as the base shear forces and the maximum moment values at each story level will be determined.

    1. Pile Response

      1. (b) (c)

        Fig. 3 Shear stresses along the pile height for loose sand for (a) Loma, (b)

        Hollister, and (c) Coyote lake earthquakes

        (a) (b) (c)

        Fig. 4 Shear stresses along the pile height for medium sand for (a) Loma, (b) Hollister, and (c) Coyote lake earthquakes

        1. (b) (c) Fig. 7 Variation of horizontal displacement along the pile length for medium

          Fig. 5 Shear stresses along the pile height for dense sand for (a) Loma,

        2. Hollister, and (c) Coyote lake earthquakes

        The plate model (P-Model) overestimated the shear stresses along with the pile height when compared to the pile spacing Ls= 1.5, 2, and 2.5 m. Therefore, the maximum shear stresses attained in the three embedded row models (EPR-Models) were smaller than the value of the ratio of the predefined axial skin resistance (Tmax) to the perimeter of the pile. On the contrary, for a pile spacing Ls=1 m, the results showed that for loose and medium soils, the maximum shear stresses attained in the embedded pile were exactly equal to this ratio. This proves that the maximum shear stresses attained 100% of the input parameter, and thus equal maximum shear stresses at the pile tip were obtained for both features.

        Examining the shear stresses along the pile height for different Ls while varying the soil type and the earthquake input motion, it is well identifiable that whenever Ls increases, the shear stresses decrease (Fig. 3 to Fig. 6). This is due to the fact that when Ls decreases, the interface stiffness factor ISF for pile-soil will decrease causing a decrease in the soil stiffness, and thus less shear forces will be transferred to the piles resulting in low shear stresses.

        The maximum shear stress for each pile spacing Ls is getting reduced as a function of Ls=1 according to the following formula that was figured out from the study:

        (Ls)= % ( 1/Ls * 100) * (Ls = 1)

        Fig. 6 Variation of horizontal displacement along the pile length for loose sand

        sand

        Fig. 8 Variation of horizontal displacement along the pile length for dense

        sand

        TABLE IV RATE OF VARIATION OF HORIZONTAL DISPLACEMENTS OF PILES BETWEEN EPR AND P MODELS

        16

        % Difference (with respect to EPR model)

        Loose Sand

        Medium Sand

        Dense Sand

        Ls

        1

        1.5

        2

        2.5

        1

        1.5

        2

        2.5

        1

        1.5

        2

        2.5

        Loma

        -14

        -19

        -20

        -22

        15

        11

        15.8

        20.4

        13.2

        15.6

        15

        Hollister

        54.8

        80

        78

        54.5

        47

        26

        33.5

        34

        8.5

        9.6

        9.8

        9.8

        Coyote Lake

        33

        46.5

        47.7

        12

        10

        8

        7.45

        7.3

        1.02

        1.04

        1.07

        1.3

        TABLE V RATE OF VARIATION OF MOMENTS OF PILES BETWEEN EPR AND P MODELS

        % Difference

        Loose Sand

        Medium Sand

        Dense Sand

        Ls

        1

        1.5

        2

        2.5

        1

        1.5

        2

        2.5

        1

        1.5

        2

        2.5

        Loma

        27.5

        54.2

        72.7

        97

        22

        59.6

        72.6

        99

        15

        36.3

        59.7

        85

        Hollister

        53

        78.1

        84.6

        91

        45.4

        71.6

        89

        97

        37.8

        49

        62.6

        71

        Coyote Lake

        59.7

        79.6

        85.6

        93

        49.8

        73.1

        90.4

        98

        40

        50

        63.4

        72

        For the horizontal displacement, the plate overestimated the values for all the cases, except for the case of Loma earthquake in loose sand, where the plate underestimated the displacements by 14%, 19%, 20%, and 22% for Ls= 1, 1.5, 2, and 2.5 m respectively (Fig. 7 to Fig. 8). The percentage difference for the other cases are shown in TABLE IV. A similar behavior was witnessed for the moment values along the piles height, where the plate overestimated the values in all

        cases as shown in TABLE V. As for the variation of pile spacing (Ls), the shear stresses and the moment values increase as Ls decreases, and vice versa.

    2. Building Response

    For the peak horizontal acceleration, the plate overestimated the values for loose and medium soils under the influence of the three earthquake input motions. An overestimation occurred with an average percentage difference of 24.36%, 37.35%, and 33% for loose sand, and with 57.16%, 41%, and 48.7% for medium sand for Loma, Hollister, and Coyote Lake respectively. As for the dense sand, a negligible difference was witnessed in all cases, where the plate and the four embedded pile models recorded approximately equal horizontal accelerations (TABLE VI). Moreover, for the influence of Ls, it was noticed that changing Ls had no effect on the acceleration values, where the models with different Ls showed the same accelerations. This justifies the close percentage difference between the plate and the embedded pile models (TABLE VI).‌

    % Difference

    Loose Sand

    Medium Sand

    Dense Sand

    Ls

    1

    1.5

    2

    2.5

    1

    1.5

    2

    2.5

    1

    1.5

    2

    2.5

    Loma

    28

    23.5

    21

    24

    59.5

    57.9

    56.7

    54.5

    7

    6.8

    6.6

    6

    Hollister

    39.4

    38.4

    37

    34

    43.5

    41.5

    40

    39

    4

    3.5

    3.7

    3.6

    Coyote Lake

    33.7

    31.8

    34

    33

    48.4

    49.1

    48.7

    48.5

    6

    6.2

    6.3

    6.3

    % Difference

    Loose Sand

    Medium Sand

    Dense Sand

    Ls

    1

    1.5

    2

    2.5

    1

    1.5

    2

    2.5

    1

    1.5

    2

    2.5

    Loma

    28

    23.5

    21

    24

    59.5

    57.9

    56.7

    54.5

    7

    6.8

    6.6

    6

    Hollister

    39.4

    38.4

    37

    34

    43.5

    41.5

    40

    39

    4

    3.5

    3.7

    3.6

    Coyote Lake

    33.7

    31.8

    34

    33

    48.4

    49.1

    48.7

    48.5

    6

    6.2

    6.3

    6.3

    TABLE IV RATE OF VARIATION OF HORIZONTAL ACCELERATION BETWEEN EPR AND P MODELS

    % Difference

    Loose Sand

    Medium Sand

    Dense Sand

    Ls

    1

    1.5

    2

    2.5

    1

    1.5

    2

    2.5

    1

    1.5

    2

    2.5

    Loma

    5.64

    8.26

    6.9

    -13.4

    12

    13

    12

    11

    0.5

    0.4

    1.2

    1

    Hollister

    29

    -53.3

    -51.3

    -55

    13

    -57.3

    21

    22

    19

    19

    1.7

    2.4

    2.8

    2.9

    Coyote Lake

    53

    9.74

    7.7

    7.7

    -15.2

    5.5

    6.6

    7.4

    7.8

    0.7

    0.7

    0.7

    0.7

    2.4

    % Difference

    Loose Sand

    Medium Sand

    Dense Sand

    Ls

    1

    1.5

    2

    2.5

    1

    1.5

    2

    2.5

    1

    1.5

    2

    2.5

    Loma

    5.64

    8.26

    6.9

    -13.4

    12

    13

    12

    11

    0.5

    0.4

    1.2

    1

    Hollister

    29

    -53.3

    -51.3

    -55

    13

    -57.3

    21

    22

    19

    19

    1.7

    2.8

    2.9

    Coyote Lake

    53

    9.74

    7.7

    7.7

    -15.2

    5.5

    6.6

    7.4

    7.8

    0.7

    0.7

    0.7

    0.7

    TABLE V RATE OF VARIATION OF HORIZONTAL DISPLACEMENT BETWEEN EPR AND P MODELS

    Regarding the horizontal displacement results, a similar behavior to the horizontal acceleration was observed for medium and dense soil, where the plate overestimated the displacements in medium sand, and a negligible difference was witnessed in the dense case (TABLE V). As for loose sand, the earthquake frequency influenced the results in a different way. For Loma earthquake, the plate overestimated the displacements when compared to Ls= 1, 1.5, and 2 m (5.64%, 8.26%, and 6.9% respectively), whereas for Ls= 2.5 m, an underestimation occurred by 13.4%. On the contrary, the plate underestimated the displacements when subjected to Hollister earthquake for Ls corresponding to 1.5 and 2 m by 51.3% and 55% respectively. As for Ls= 1 and 2.5 m, no precise trends in the results were observed as shown in TABLE V. Moreover, an overestimation under Coyote Lake was witnessed for all cases except for Ls= 2.5 m, where a variable trend in the results occurred. Hence, the plate overestimated the horizontal displacements when the soil is

    medium to dense sand. However, for a loose sand, a variable trend in the results still exists. In addition, the pile spacing (Ls) has no influence on the results in cases of medium and dense sand, whereas for loose soil, a significant effect is monitored.

    For the shear forces and moment values, the plate underestimated the base shear for Loma earthquake (TABLE

    VIII) and overestimated the values for Hollister and Coyote Lake (TABLE IX and TABLE X). As for the influence of pile spacing (Ls) on the base shear values, it was witnessed that as Ls increases, base shear increases for loose sand and decreases for medium sand. A negligible difference was observed for dense sand case, where the plate and the four embedded pile row models gave approximately equal base shear forces. As for the shear forces and moment values along the building height and precisely for the story levels ranging between 36 and 72 m, the plate underestimated the results in loose sand and overestimated them in medium sand in the three types of earthquakes. The results are actually depending on a complex interaction between the pile distances (Ls) and the earthquake frequency, which led to such a variation in the shear and moments.

    TABLE VIII RATE OF VARIATION OF BASE SHEAR FORCES BETWEEN EPR AND P MODELS FOR LOMA EARTHQUAKE

    Plate Model

    Ls

    Base Shear Vb (KN/m)

    1

    1.5

    2

    2.5

    Loose Sand

    -7.04

    -9.48

    -12.1

    -12.47

    -13.34

    % Difference

    34.6

    72.5

    77.13

    89.5

    Medium Sand

    -6.67

    -10.8

    -10.6

    -9.29

    -7.69

    % Difference

    62.2

    59

    39.28

    15.3

    Dense Sand

    -8.54

    -8.95

    -8.7

    -8.46

    -8.32

    % Difference

    4.8

    1.6

    -0.94

    -2.58

    TABLE IX RATE OF VARIATION OF BASE SHEAR FORCES BETWEEN EPR AND P MODELS FOR HOLLISTER EARTHQUAKE

    Plate Model

    Ls

    Base Shear Vb (KN/m)

    1

    1.5

    2

    2.5

    Loose Sand

    4.42

    1.145

    -0.84

    -2.61

    -2.44

    % Difference

    -74.1

    -81

    -40.9

    -44.8

    Medium Sand

    3.54

    -2.61

    -1.49

    -0.58

    0.071

    % Difference

    -26.2

    -57.9

    -83.6

    -98

    Dense Sand

    -8.31

    -9.06

    -8.78

    -8.59

    -8.42

    % Difference

    9.03

    5.67

    3.37

    1.32

    Plate Model

    Ls

    Base Shear Vb

    (KN/m)

    1

    1.5

    2

    2.5

    Loose Sand

    3.41

    1.1

    -1.06

    -2.3

    -3

    % Difference

    -67.74

    -68.91

    -32.5

    -12

    Medium Sand

    3.36

    -2.81

    -1.67

    -0.77

    -0.06

    % Difference

    -16.37

    -50.3

    -77

    -98

    Dense Sand

    -8.21

    -8.97

    -8.69

    -8.49

    -8.3

    % Difference

    9.3

    5.85

    3.41

    1.47

    Plate Model

    Ls

    Base Shear Vb

    (KN/m)

    1

    1.5

    2

    2.5

    Loose Sand

    3.41

    1.1

    -1.06

    -2.3

    -3

    % Difference

    -67.74

    -68.91

    -32.5

    -12

    Medium Sand

    3.36

    -2.81

    -1.67

    -0.77

    -0.06

    % Difference

    -16.37

    -50.3

    -77

    -98

    Dense Sand

    -8.21

    -8.97

    -8.69

    -8.49

    -8.3

    % Difference

    9.3

    5.85

    3.41

    1.47

    TABLE X RATE OF VARIATION OF BASE SHEAR FORCES BETWEEN EPR AND P MODELS FOR COYOTE LAKE EARTHQUAKE

    To conclude, this study assessed the reliability of designing the piles as plate element in capturing the real structural-pile seismic response upon comparing it with modeling piles as embedded row elements. The results proved the inadequacy of the use of plate model in predicting the pile seismic response. As for the structural seismic response, an overestimation of the horizontal displacements and a variation in the shear forces and moments were detected by the plate model in cases of loose and medium sand. Therefore, the use of plate model is adequate only in case of dense soil, where it can be able to capture the real structural seismic response. The final structural-pile response was therefore the result of an intricate interaction between the pile distances (Ls) and the soil type under the earthquake characteristics (the frequency and the accelerogram).

  5. CONCLUSION

The main goal of this study was to investigate the reliability of modeling the pile as a plate element in a dynamic SSI problem. This was achieved by comparing it to the pile when modeled as an embedded pile row that is acknowledged as being able to accurately simulate the real SSI behavior. This comparison was conducted in terms of seismic responses of pile and structure. A series of numerical models was generated taking into consideration several parameters that might influence the SSI analysis. The spacing between piles (Ls) is disregarded when modelling the pile as a plate element. Therefore, the effectiveness of this model was measured by comparing the structural-pile response with four embedded pile row models having different Ls (1, 1.5, 2, and 2.5 m). The analysis was carried out for different soil types and earthquake input frequency contents. The obtained results show that:

  1. Pile Response

    • The plate model overestimated the shear stresses along

      interaction between the pile distances (Ls) and the earthquake frequency content, which led to such a variation in the shear.

      • In dense sand, a negligible difference in the results of the building response was recorded between the plate and embedded row, despite all the variation in parameters. This means that the plate model could be safely employed.

      Based on the above findings, it is recommended to use the embedded row feature for conducting a real structural-pile performance, especially for loose and medium sands. The plate model cannot be used when designing piles whatever the soil type is since it does not accurately represent the piles real performance, and it could even provide detrimental results in some cases. Yet, if the objective is the structural behavior, this study proved that the plate model can be safely used in case of dense sandy soils only.

      REFERENCES

      1. EI-Mossallamy Y. (1999) Load settlement behavior of large diameter bored piles in overconsolidated clay. Proceedings NUMOG VII Graz, Balkema Rotterdam.

      2. Engin, H.K. 2007. Report on tension pile testing using embedded piles. Plaxis internal report. Delft (The Netherlands).

      3. Engin H.K., Septanika E.G. and Brinkgreve R.B.J. 2007. Improved embedded beam elements for the modelling of piles. Proc. 10th Int. Symp. on Numerical Models in Geotechnical Engineering NUMOG X, Rhodes (Greece). April 2007.

      4. Engin, H.K., Septanika, E.G., Brinkgreve, R.B.J.& Bonnier, P.G. 2008a. Modeling piled foundation by means of embedded piles. In Karstunen & Leoni (eds), Geotechnics of Soft Soils: Focus on Ground Improvement; Proceedings of the 2nd International IWGSS Workshop, Glasgow, Scotland, September 3-5, 2008. London, Taylor&Francis.

      5. Engin, H.K., E.G. Septanika & R.B.J. Brinkgreve 2008b. Estimation of pile group behaviour using embedded piles. In Singh (ed), International Association for Computer Methods and Advances in Geomechanics;

        12th International IACMAG Conference, Goa, India, October, 1-6, 2008: 3231-3238.

      6. Sluis, J., Besseling, F., & Stuurwold, P. (2014). Modelling of a pile row

        the pile height when compared to the three embedded row models having Ls of 1.5, 2, and 2.5 m respectively. The rate of variation

      7. in a 2D plane strain FE-analysis.

        Dao, T. (2011). Validation of plaxis embedded piles for lateral loading. Master of Science Thesis, Delft University.

        grows with the increase of Ls, which proves that neglecting the pile spacing leads to irrelevant performance.

        • The plate model overestimated the moment values along

      8. Kwaak, B. v. d. (2015). Modelling of dynamic pile behaviour during an

        earthquake using PLAXIS 2D: Embedded beam (rows). (Master of Science), Delft University of Technology, Delft, Netherlands.

      9. Septanika E. G. 2005b. Validation testing embedded pile in Plaxis 3D

        the pile height for all soil types under the influence of all earthquake input motions.

      10. Foundation. Plaxis internal report. Delft (The Netherlands).

        Sluis, J. (2012). Validation of embedded pile row in PLAXIS 2D. Delft University of Technology, Delft.

        • No clear trend was observed in the horizontal displacements of the piles where the plate provided detrimental results. This is due to the complex interaction between the soil

      11. Lysmer, J., Kuhlemeyer, R. L. (1969). Finite Dynamic Model for Infinite Media. Journal of Engineering Mechanics Division, 95 (4), 859878.

      12. Kuhlemeyer, R.L. and Lysmer. J. (1973) Finite Element Method Accuracy for Wave Propagation Problems. Journal of the Soil Dynamics

        type and the frequency content of the earthquake.

  2. Building Response

    • The plate overestimated the peak horizontal acceleration for loose and medium soils. Changing Ls has no influence on the acceleration values.

    • The plate overestimated the peak horizontal displacements for all earthquake input motions in medium sand, whereas for loose sand, a variable trend was observed. Changing Ls has no effect on the results in cases of medium and dense soils, whereas a significant effect was witnessed in case of loose sand.

    • The plate underestimated the base shear for loose and medium sand under the influence of Loma earthquake, whereas it overestimated the values under the excitation of Coyote Lake and Hollister earthquakes. The results are actually depending on the

Division, 99, 421-427.

Hudson, M., Idriss, I.M., & Bekaie, M.(1994). QUAD4M – A Computer Program to Evaluate the Seismic Response of Soil Structures Using Finite Element Procedures Incorporating a Compliant Base. Center for Geotechnical Modeling , Dept. of Civil and Environmental Engineering, Univ. of California., Davis, California.

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