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1 Introduction

A relative movement between pile and the soil leads to mobilize shear stresses along the interface between pile and adjacent soil. The main reason behind such movement is the application of surcharge load on the ground surface next to pile. Terzaghi and Peck (1948) assumed full mobilization of shear strength along the pile-soil interface up to the pile toe for a single pile, or along the perimeter of pile group. Therefore, the neutral point (point of zero shear stress) is assumed to be located at the bearing stratum of the pile. Indraratna et al. (1992) suggested that in order to minimize NSF, piles might be driven few week, or a month after applying the surcharge load on the ground surface.

Bipul et al. (2003) presented a constitutive relationship for one-dimensional consolidation of clays. They recognized the importance of structural viscosity on clay consolidation. The viscous effect through consolidation is less at initial stage, and likely to increases gradually along with the progress of consolidation. Hanna and Sharif (2006) conducted a study on piles driven into clay and subjected to indirect loading through the surcharge applied symmetrically on the surrounding area. The study was based on a numerical model using a finite element technique and the soil was assumed to follow a linear elastic-perfectly plastic stress-strain relationship, which defined by Mohr-Coulomb failure criterion. They concluded that negative friction is developed on the pile’s shaft during the undrained period and continues to exist until the consolidation of the surrounding soil be fully completed under surcharge loads. Tung-Lin (2009) studied the effect of viscosity on consolidation of poroelastic soil due to groundwater table depression. He showed that the displacement and pore water pressure of clay stratum are strongly related to the viscosity effect. The overestimation of soil displacement will occur only when the viscosity effect is being neglected. Werjuan et al. (2012) studied NSF of the super long pile caused by soil settlement under large-scale surcharge loading. They showed the impact of NSF and to what extent the soil parameters surrounding pile affect the NSF distribution. In their series of model tests on NSF on single pile and pile groups under different surcharge loading conditions, Ting et al. (2016) found that pile head settlement and NSF under side load were smaller compared with the result of the test under uniform loading, while the location of neutral plane (LNP) was lower. Arpan and Sujit (2017) developed a 3-D consolidation apparatus and performed a series of 3-D consolidation test under different surcharge pressures. They concluded that the consolidation characteristics were largely affected by the surcharge pressure. Increasing the surcharge on the surrounding soil makes it denser to reduce both the lateral movements of soil particles, and the lateral pore water pressure.

Many researchers studied the effect of surcharging on the NSF distribution, however the objective of this paper is to study the effect of the combination of surcharging and pile load on the distribution of shear stresses along the pile length besides the effect of viscosity during primary consolidation compared to elastic-plastic behavior. An elastic-viscoplastic and elastic-plastic soil models were represented herein to carry on the parametric study. A field test of a single pile was used to validate the model and conduct the numerical study.

2 Methodology

2.1 Field Loading Test

Matsui (1993) carried out a full-scale loading test of a cast-in-place RC bored pile in Osaka bay, Osaka, Japan. The soil profile consisted of both Holocene Deposits and Upper Pleistocene Deposits. The Holocene layers consisted of loose and soft silts and clays. A sandy gravel layer was adopted as a bearing layer of the tested pile. The tested pile was a cast-in-place RC pile with 1.5 m in diameter and 28.5 m in length. The vertical loading test was carried out, in accordance with the Standard of the JGS (JGS 1972). Figure 1 shows the field test soil section.

Fig. 1.
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Field test section

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2.2 Numerical Model

2.2.1 Soil Constitutive Models

Finite element analysis was performed in order to compare results obtained from field test measurements with those from the numerical model. The model is an axisymmetric model assumes to behave as elastic-plastic material to represent the correlation between the stresses and the strains due to Matsui and Abe (1981) constitutive soil model for the main clay layer. This elastic-plastic soil model will be compared with the elastic-viscoplastic soil constitutive model represented by Sekiguchi and Ohta (1977). The different between these two soil models is the time dependency. Although elastic-plastic soil model is a time-dependent stress strain model but the viscous effect has been noticed during primary consolidation which affected the soil settlements. Elastic-plastic model is represented by Matsui-Abe in Eqs. (1) and (2). The Sekiguchi-Ohta model is a Cam-Clay type effective stress model for the behavior of clay-type soils and the yield surface (f) is given by Eq. (3). The bearing layer behavior was represented by Yasufuku model in Eq. (4).

$$ \begin{aligned} & e_{0} - e = \lambda \ln \left( {\frac{{p^{\prime}}}{{p^{\prime}_{0} }}} \right) + \left( {\lambda - \kappa } \right)\left( {\frac{{\alpha_{a} }}{{\alpha_{a} - 1}}} \right)\ln \left\{ {\frac{{M_{a} + (\alpha_{a} - 1)\eta }}{{M_{a} + (\alpha_{p} - 1)\eta_{k0} }}} \right\} \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad {\text{For the active state}} \\ \end{aligned} $$
(1)
$$ \begin{aligned} & e_{0} - e = \lambda \ln \left( {\frac{{p^{\prime}}}{{p^{\prime}_{0} }}} \right) + \left( {\lambda - \kappa } \right)\left( {\frac{{\alpha_{p} }}{{1 - \alpha_{p} }}} \right)\ln \left\{ {\frac{{M_{p} + (1 - \alpha_{p} )\eta_{k0} }}{{M_{p} + (1 - \alpha_{p} )\eta_{{}} }}} \right\} \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad {\text{For the passive state}} \\ \end{aligned} $$
(2)

where e is the void ratio, e0 is the initial value of e, λ is the compression index, κ is the swelling index and \( \alpha_{a} \), \( \alpha_{p} \) are the strain increment ratio.

$$ f = \mu \ln \left| {\frac{1}{\delta }\left[ {\left\{ {1 - \exp \left( { - \frac{{\delta \dot{v}_{r}^{v} }}{\mu }t} \right)} \right\}\exp \left( {\frac{{v^{p} }}{\mu }} \right) + \delta \exp \left( { - \frac{{\delta \dot{v}_{r}^{v} }}{\mu }t} \right)} \right]} \right| - v^{vp} = 0 $$
(3)

where μ is the coefficient of secondary consolidation, \( \dot{v}_{r}^{v} \) is the reference viscous volume strain rate, δ is a material constant and \( v^{p} \) is the plastic volumetric strain.

$$ f = \ln \frac{p}{{p_{0} }} + \frac{C}{2(C - 1)}\ln \left[ {\frac{{(1 - C)(2\alpha - \eta )\eta + \left\{ {N - (2 - C)\alpha } \right\}N}}{{(1 - C)\alpha^{2} + \left\{ {N - (2 - C)\alpha } \right\}N}}} \right] = 0 $$
(4)

model in Eq. (4)

Where Ν and C are experimental parameters, α is an internal parameter to reflect the influence of the proportional loading path on the yield surface and \( \upeta = \frac{q}{{p^{\prime}}} \) is the stress ratio.

2.2.2 Model Boundary, Mesh and Initial Conditions

The surface of the top layer is assumed to be permeable while the low and side boundaries of the model are supposed to be impermeable. The level of the ground water is at 0.80 m down from the surface. The low model boundary is being fixed, while the boundaries at the axis of symmetry and sides are free to move vertically.

The mesh was divided into 13 blocks. The first block -the pile- is divided into 360 elements behave as elastic material. The main clay layer includes block (2) and block (3) which both are divided into 234 elements. The abruption between pile shaft and surrounding soil is represented by 36 joint elements (Goodman et al. 1968) in which the main clay layer includes 6 joint elements. Figure 2 shows the analytical study model and mesh boundary.

Fig. 2.
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Numerical model and the mesh

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2.3 Model Validating

Numerical modelling using the finite elements technique was used herein to validate the used model. Table 1 shows the analytical elastic parameters for the pile material. Table 2 describes the basic mechanical constants for clay in Elastic-plastic behavior by Matsui-Abe. The main parameters for Sekiguchi-Ohta model are mentioned in Table 3 Yasufuku basic parameters for the bearing soil layer are shown in Table 4. Finally, the parameters of joint elements for the main clay layer are shown in Table 5. All parameters were determined through soil investigations including SPT and CPT (after Oda 2012).

Table 1. Analytical parameters of elasticity
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Table 2. Analytical parameters of Matsui-Abe model
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Table 3. Analytical parameters of Sekiguchi-Ohta model
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Table 4. Analytical parameters of Yasufuku model
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Table 5. Analytical parameters of joint elements
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A comparison between the measured axial forces and predicted values by the present numerical model is shown in Fig. 3. It can be noticed from the comparison results that the numerical model is valid to carry on the parametric study.

Fig. 3.
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Pile axial load distribution

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3 Parametric Study

The aim of this parametric study is to examine different types of loading, to observe the behavior of both soil and pile, and to study the loading cases effect on settlements and skin friction distribution. The study is based on two types of loading;

  1. ①

    S: First, applying the pile load and then applying the surcharge load on the ground surface next to pile head (i.e. no surcharging on pile).

  2. ②

    P + S: First, applying the pile load and then applying the surcharge load on both ground surface and pile head (i.e. all model surface is under surcharging).

In the light of these two types of loading, Table 6. was found to clarify the parametric study of loading cases.

Table 6. Loading cases for the parametric study
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The following figures present the effect of loading and viscosity on the settlements, axial force and skin friction distribution. Figure 4 shows the pile axial load distribution for elastic-viscoplastic model. When applying a small value of surcharging, larger distribution was examined along pile’s shaft in regarding to comparing viscosity with elastic-plastic. In the contrary, in the light of large surcharging, the difference in the distribution in two models did not occurred. A comparison of the case of small and large surcharging in two soil models is shown in Fig. 5.

Fig. 4.
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Pile axial load distribution/elastic-viscoplastic model

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Fig. 5.
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Pile axial load distribution/comparison between elastic-plastic and elastic-viscoplastic model

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The ground settlements with time for the two soil models and different cases of loading are shown in Figs. 6 and 7. Viscous effect had a major influence on soil settlements, where this influence played a rule in case of applying a small surcharging while bigger surcharge load leaded to a small different in the settlements values between elastic-plastic and elastic-viscoplastic soil models and that is clarified in Fig. 8. Changing the applied pile load to a specific value occurred the pile to settle more than the ground, whereas this conclusion can be shown in Figs. 9 and 10 for two cases of pile loading.

Fig. 6.
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Ground settlements with time/elastic-plastic model

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Fig. 7.
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Ground settlements with time/elastic-viscoplastic model

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Fig. 8.
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Ground settlements with time/comparison between elastic-plastic and elastic-viscoplastic model

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Fig. 9.
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Ground and pile settlements with time/PL = 100_SL = 02 (S)

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Fig. 10.
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Ground and pile settlements with time/PL = 1100_SL = 02 (P + S)

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As the distribution of skin friction is related to pile and soil settlements, same conclusion was observed in Figs. 11 and 12, whereas applying a small surcharge load leaded to a bigger skin friction distribution in case of viscosity. Figure 13 shows the case of applying a larger pile load which changed the distribution of NSF into a positive skin friction.

Fig. 11.
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Shear stress distribution/comparison between elastic-plastic and elastic-viscoplastic model (PL = 100_SL = 02(S))

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Fig. 12.
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Shear stress distribution/comparison between elastic-plastic and elastic-viscoplastic model (PL = 100_SL = 08 (S))

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Fig. 13.
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Shear stress distribution/comparison between elastic-plastic and elastic-viscoplastic model (PL = 1100_SL = 02(P + S))

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4 Conclusions

Surcharging and pile load play a vital role in mobilizing shear stresses along the pile’s shaft (negative and positive friction) regardless the used soil model in analysis. In this paper two different soil models were used and a parametric study for different loading cases was mentioned. It can be concluded that:

  • Surcharging is the main reason of soil settlements and NSF mobilizing and its effect will be more significant when it’s applied only on the ground surface next to the pile.

  • When the whole model surface is under surcharging and the pile head is loaded, the NSF will be smaller comparing with the case of surcharging is applied on the ground surface only. Adding an extra load to the pile, leads the pile at specific point to settle equal or more than the adjacent soil which reduces NSF.

  • Viscous effect has a major role in increasing the soil settlements and skin friction distribution even though the study has been done during the primary consolidation stage. This effect will be noticed clearly in case of small values of surcharging but when the surcharge load exceeded a specific amount, the viscous influence was approximately similar to elastic-plastic.

  • It is important to take the viscous effect into consideration when designing pile foundations. Carrying on this study to examine the soil behavior and skin friction distribution during secondary consolidation due to structural viscosity is also important and must be covered through future researches.