FINITE ELEMENT SIMULATION OF PLUGGED OPEN ENDED PILE BEHAVIOR

Open-ended steel pipe piles are widely used for foundations both on land and offshore because of low cost compare with other types of piles and it does not need a high effort for driving. During driving process of these piles into the soil, a soil column known as the soil plug is formed inside the pile. As the penetration continues, the frictional resistance between the inner pile shaft and the soil plug may be developed and in turn may prevent further soil intrusion. Depending on the relative movement between the pile and the soil plug, the pile is considered to be perfectly plugged, imperfectly plugged or unplugged . A numerical modeling of experiments was carried out using PLAXIS-2015 software, in which the Hardening Soil Model (HS small) has been used for soil modeling. During the verification problem used to simulate the experimental results of the pile group G2(2x2), the piles simulated as volume piles and steel cap were modeled using linear elastic model. The simulation showed that the maximum percentage of deviation between experimental and theoretical results is not more than 13.0%. This ratio is considered good when compared to the actual results and the theoretical results with the same values in some of the results.


INTRODUCTION
After an open-ended pile is driven into the ground, a soil plug may progress within the pile during driving, which may avoid or partially constrain additional soil from incoming the pile.
It is known that the driving resistance and the bearing capacity of open-ended piles are administered to a large extent by this plugging effect. The design principles for open-ended piles, depend on field tests, chamber tests or systematic methods, have been studied, (Klos and Tejchman, 1977;American Petroleum Institute, API-1991;Randolph et al., 1991;Jardine et al., 1998). These principles are usually used for offshore foundation design, the bearing capacity of an open-ended pile able only be appreciation for either the completely coring mode or the fully plugged style of breakthrough.
Formation of a soil plug in an open-ended pile is a very important factor in determining pile behavior both during driving and during static loading. Most open-ended piles drive in coring mode but are plugged during static loading. On some occasions, piles may plug and impede driving. If the available pile hammer cannot drive the pile to the design depth, a problem may arise, particularly for piles with thickened walls near the surface or mud line, such as piles used to resist lateral loading (Murff et al., 1990). The formation of a soil plug in an open-ended pile is a very important factor in determining pile behavior both during driving and during static loading. The degree of soil plugging can be represented by the incremental filling ratio, defined as (Iskander, 2010). Paikowsky and Whitman (1990) investigated the effect of soil plugging on the axial resistance developed by open-ended (pipe) piles installed in sand and clay. They described the process of soil plug formation during the initial stages of pile installation, the length of the soil plug (Lp) inside the pipe equals the pile penetration depth (L), and the pile is said to be coring (IFR =100%). As the pile penetration depth increases, frictional stresses between the inside wall of the pile and the soil plug may cause partial plugging (0% > IFR, 100%), and in some cases the pile may become completely plugged (IFR = 0%). They noted that plugging resulted in a large increase in the axial resistance of piles installed in sand and caused a large increase in the zone of excess pore water pressure surrounding piles in clay, causing a delay .The development of the soil core during installation is quantified by the plug length ratio (PLR) as equation (1) or the incremental filling ratio (IFR) in equation (2):  tested a model pile made of two very smooth stainless steel pipes with different diameters. It had an outside diameter of 42.7 mm, an inside diameter of 36.5 mm, and a length of 908 mm. Paik and Salgado explained the relationship between the plug length ratio (PLR) and IFR for the chamber calibration test, and it can be expressed as follows in equation (3):

BASE LOAD CAPACITY OF AN OPEN TUBULAR PILE
A small introduction to the basic load bearing capacity of an open tubular pile seems in place.
The basic load-bearing capacity of an open tubular pile is composed of the tip resistance under the ring-shaped tip the pile and the internal friction in the post, which is generated by the soil which enters the post during the installation. The last of these two components is commonly referred to as the load bearing capacity of the soil plug. On this basis, the following formulation base load-bearing capacity is given as follows in equation (4): where: Qb= base load capacity of the pile, It is clear in Fig. 1-b situation, namely, an open tubular pile without plug formation, less soil displacement brings than c situation where the open tubular pile has already been partially plugged. These higher ground displacements logically also brings greater radial tensions. There is therefore provided that, as shown in field trials (Kishida, 1967;, laboratory tests in test chambers (O'Neill and Raines, 1991;Foray et al., 1998, Fattah et al., 2016, and centrifuge tests on model piles and open tubular pile a reaction brings about that is located between those of a pile and a soil displacement drilled pile.
The objectives of this paper is to offer a better realization regarding the performance of pipe pile group under vertical loading with soil plug, and to provide valuable geotechnical data and parameters necessary for the numerical simulations and foundation design.

NUMERICAL MODELING OF PIPE PILES
The methods of analysis, which use the finite element technique, will be discussed in this study.
The finite element method represents one of the extensive proliferation techniques in the representation of engineering applications (PLAXIS Manual, 2015). The review of equations that are concerned with the program of Plaxis-3D (2015) and how to build mathematical models depending on the soil type also will be discussed with details in this study. It also includes a verification process for the case of group piles (4-piles) driven in sandy soil and tested by the laboratory model. After fixing the soil properties in the theoretical model through the verification, which will be explained in this study. Full numerical analysis approach, attempts are made to satisfy all theoretical requirements, including realistic soil constitutive models and boundary conditions that realistically simulate field conditions. Approaches based on finite difference, boundary element and finite element methods are those most widely used. These methods essentially involve computer simulation of the history of the boundary value problem from field conditions, through construction in the long term. Their ability to reflect accurately the field conditions essentially depends on the ability of the constitutive model to represent real soil behavior and correctness of the boundary conditions imposed (PLAXIS Manual, 2015).

PLAXIS-3D 2015 SOFTWARE
In PLAXIS 2015 (3D), complex geometry of soil and structures can be defined in two different modes. These modes are defined specifically for soil or structural modeling. Independent solid models can automatically be intersected and meshed

HARDENING SOIL MODEL BEHAVIOR (HS)
The hardening soil model is an advanced model for the simulation of soil behavior. As for the Mohr-Coulomb model, limiting states of stress are described by means of the friction angle, , the cohesion, c, and the dilatancy angle, ψ. However, soil stiffness is described much more accurately by using three different input stiffnesses: the triaxial loading stiffness, E50, the triaxial unloading stiffness, Eur , and the oedometer loading stiffness, Eoed . As average values for various soil types, Eur≈ 3E50 and Eoed≈ E50 are suggested as default settings, but both very soft and very stiff soils tend to give other ratios of Eoed /E50, which can be defined. In contrast to the Mohr-Coulomb model, the Hardening Soil model also accounts for stress-dependency of stiffness moduli. This means that the stiffness increases with pressure. Hence, all three input stiffnesses relate to a reference stress, usually taken as 100 kPa (O'Neill, and Raines (1991).
The hardening soil model with small-strain stiffness (HSsmall) is a modification of the above hardening soil model that accounts for the increased stiffness of soils at small strains. At low strain levels, most soils exhibit a higher stiffness than at engineering strain levels, and this stiffness varies non-linearly with strain. This behavior is described in the HSsmall model using an additional strain-history parameter and two additional material parameters, i.e. 0 and 0.7 . 0 is the small-strain shear modulus and 0.7 is the strain level at which the shear modulus has reduced to about 70% of the small-strain shear modulus (Iskander, 2010). The advanced features of the HSsmall model are most apparent in working load conditions. Here, the model gives more reliable displacements than the HS model. When used in dynamic applications, the hardening soil model with small-strain stiffness also introduces hysteretic material damping Kufa Journal of Engineering, Vol. 8, No. 2, 20177 (Józsa, 2011. The hardening soil model, however, supersedes the hyperbolic model by far: Firstly by using the theory of plasticity rather than the theory of elasticity, secondly by including soil dilatancy and thirdly by introducing a yield cap. Some basic characteristics of the model are (Plaxis Manual, 2015) in Table 1: For oedometer conditions of stress and strain, the model implies for example the relationship = ( ⁄ ) . In the special case of soft soils it is realistic to use m = 1. In such situations there is also a simple relationship between the modified compression index * , as used in models for soft soil and the oedometer loading modulus in equation (5) Where p ref is a reference pressure. Here we consider a tangent oedometer modulus at a particular reference pressure p ref .
For the sake of convenience, restriction is made here to triaxial loading conditions with ′ 2 = ′ 3 and ′ 1 being the major compressive stress. Moreover, it is assumed that q <qf, as also indicated in Fig. 2. It should also be realised that compressive stress and strain are considered negative (Schanz et al., 1999).

PARAMETERS OF THE (HSSMALL) MODEL
This model is, as the name indicates, a version of the hardening-soil model. Hardening-soil model with small-strain stiffness (HS small-model) is a more advanced version, with focus on describing soil's behavior more accurately while unloading and reloading the soil. The original HS-model models the stress-strain relation in this phase as linear-elastic with the stiffness .
The HS small-model requires several parameters which are generally familiar to most geotechnical engineers. The parameters can be obtained from basic tests on soil samples, these parameters with their standard units are in Table 2.

CONSTRUCTION OF THE MODEL AND MESHING
In PLAXIS (2015), the geometry is defined by vertical "boreholes" and horizontal "work planes". The work planes are used to define geometry points, geometry lines, clusters, loads, boundary conditions and structures.
When creating a geometry model, it is usual to start defining the boreholes and thus the vertical depth of the model. Vertical is defined as the y-direction. The boreholes are divided in layers, which subsequently are assigned different materials (i.e. different soil properties). When multiple boreholes are present in the model, the soil properties are interpolated between the boreholes thus creating non horizontal soil layers. The pore pressure distribution is defined in the boreholes. The distribution could be entered manually (Vermeer and Brinkgreve, 2012).

SIMULATION OF THE EXPERIMENTAL PIPE PILE GROUP MODEL (MODEL TEST)
The pipe piles are made of aluminum, while the tested soil is Karbela sand. A group of (2x2) piles are considered here as a reference for checking the numerical solution implemented by PLAXIS-3D (2015) program. The height of sand column inside the open ended piles was represented in the numerical program as measured in the experiential work depending on the driving method, where the sand columns lengths vary from 195 mm to 295 mm as shown in Table 3. Which also presents the characteristics of the situation that was taken from the cases of experimental work of Al-Gharrawi (2016).  Fig. 3.

216, 216, 295, 195 mm
The sand is modeled utilizing the (HS small) model, the parameters are listed in Table 4. The steel pile cap has dealt with as a linear elastic by given a modulus of elasticity and Poison´s ratio values.
Using PLAXIS-3D (2015) program, the mesh can be generated as three analyses were performed depending on the accuracy of problem: one with a coarse, one with a medium and one with a very fine mesh. For each one, 6 models are analyzed using different the interface elements. The Rinter coefficient values were changed from 0.1 to 1. Rinter factor which relates the interface strength (wall friction adhesion) to the soil strength (friction angle and cohesion).     Engineering, Vol. 8, No. 2, 2017 13 Ko value. The range value of the coefficient of horizontal soil stress for driven piles K/ Ko equal to (1-2) (Tomlinson, 2015).  The horizontal stress around piles will be increased with increases depth and the maximum horizontal stresses reach to about at K equal to 2 because of the stress between soil and pile will turn into passive zone.   Table 4. is not more than 13.6 %. This is a good correlation for the results especially when the coefficient of the lateral earth pressure equals to (Ko=2). The main reason for this behavior can be attributed to the technique of pile installation and to the increment of the soil lateral pressure from the pile and the soil turned to the passive case instead of at rest condition.
The inner shaft resistance is effectively mobilized during driving due to the inertia of the soil plug. Only imperfect plugging of the pipe pile occurs during driving. In the static load test, the outer shaft resistance is predominantly mobilized at initial loading stage until it reaches the ultimate state. After the outer shat resistance is fully mobilized, the inner shaft resistance starts to mobilize. 2. Hardening soil model with small strain is considered good model to represent the case of pipe pile group and get to the convergence between experimental and theoretical results by using PLAXIS-3d program.
3. It is believed that the stiffer behavior is due to installation effect that increases the soil horizontal stresses and enables larger shear mobilization. This can be introduced in the model by theoretical increasing of the initial lateral earth pressure coefficient (Ko). The