*3.3.2 Two- and three-dimensional numerical modelling*

To gain further insight into the field of simulation of the soil–pile interaction, the general design process is presented here. Finn and Fujita [108] developed and recently reviewed [109] an approximate method for nonlinear, three-dimensional analysis of pile foundations using PILE-3D. Constitutive models for simulating the nonlinear behaviour of pile in liquefiable soil have been proposed and typically implemented through the finite-element using two- or three-dimensional numerical modelling. Some of the more popular computer programs used are FLAC (Itasca), DIANA (DIANA Analysis) and PLAXIS. Many researchers have been using the Open System for Earthquake Engineering Simulation (OpenSees) (Mazzoni et al., [110]) as a ground response analysis tool. However, the main challenge of numerical modelling remains the simultaneous numerical prediction of accelerations, generation and redistribution of excess pore pressures, and the resulting of deformations [111]. Yu et al. [112] suggested that the finite element method (FEM) based on solid mechanics can accurately simulate the soil behaviour (for the initial stage) and the smoothed particle hydrodynamics (SPH) method in the framework of fluid dynamics is more suitable (for the flow stage). In this regard, Finite difference numerical models were developed using ABAQUS/Explicit, SAP2000, FLAC 3D, SANISAND and PDMY02 models or FEM using DBLEAVES code. The bounding surface constitutive model simple anisotropic sand (SANISAND) developed by Dafalias and Manzari [113] and implemented in OpenSees by Ghofrani and Arduino [114], was utilised to represent the behaviour of the liquefiable soil layer. Pressure-Dependent multiyield surface constitutive model version 02 (PDMY02) developed and implemented in OpenSees by Elgamal et al. [115] and Yang et al. [116] to simulate soil behaviour. Ramirez et al. [111] compared the predictive capabilities of PDMY02 and SANISAND platforms. Furthermore, Drucker-Prager [117] and Mohr-Coulomb plasticity [118] models are also soil constitutive modelling approaches in 3D analyses of soil-foundation systems.

Some of the recent numerical studies on pile foundations in liquefiable soil are listed in **Table 2**.

A fully coupled formulation (u–P or u–P–U) has been used to analyse soil displacements and pore water pressures [136]. The u–P formulation (called EightNodeBrick–u–P element in OpenSees framework) is the simplification of the u-p-U approach, which captures the movements of the soil skeleton (u) and the change of the pore pressure (P). More detail about description, formulation and implementation of this theory can be found in [120–122]. **Figure 10** is an example of three numerical modelling of pile in liquefiable of soil.

BNWF analyses of piles and pile groups have been exclusively employed for modelling case histories. Dash et al. [57] created 3D non-linear model of Tower of Kandla Port by using a finite element program SAP2000. A good agreement between the analytical and field observations analysis was reported. Similarly, Dash et al. [40] investigated the bending-buckling mechanism by exploring the Showa

**197**

**Table 2.**

*The Dynamic Behaviour of Pile Foundations in Seismically Liquefiable Soils: Failure…*

**Test type Soil** 

Full scale Clay

table

3D Abaqus Full scale Sandy

**type**

soil

clay

Finn [109] PILE3-D Full scale Sand 4 × 4 Concrete Free and

sands

Silica sand

Li et al. [133] 3D Flac Full scale Sand 3 × 3 XCC pile Fixed

sand

sand

Full scale silty

table

Shaking table

Shaking table

Shaking table

Shaking table

Centrifuge Ottawa

Full scale Nevada

Centrifuge Sand Single Steel

**Pile configuration**

Sand 3 × 3 Stainless

Full scale Sand Single Aluminium Free

Centrifuge Sand Single Concrete Free and

Centrifuge Sand Single Concrete Fixed

Full scale Sand Single Concrete Fixed

Full scale Sand Single Reinforced

**Pile type Pile head** 

steel

3 × 4 Concrete Fixed

Concrete

Single steel Fixed

pipe

concrete

pipes

3 × 3 Steel Fixed

concrete

pipe pile

OWT Monopile Fixed

Single Concrete Fixed

2 × 2, 4 × 4 Reinforced

Sand Single, 2 × 2 Aluminium Free and

Sand 3 × 3 Aluminium

Sand Single Reinforced

Centrifuge Sand 3 × 2 Concrete Fixed

Full scale Sand 3 × 4 Concrete Fixed

Sand Single Aluminium Free

Centrifuge Sand Single Concrete

**condition**

Fixed

Free and Fixed

Fixed

Fixed

Fixed

Fixed

Fixed

Fixed

Free and Fixed

Free

*DOI: http://dx.doi.org/10.5772/intechopen.94936*

**type**

3D (u-p-U) FEM

SAP2000

3D (p-y) FEM

3D (p-u) OpenSees

3D (p-u) OpenSees

p-y NASTRAN

2D (p-y) OpenSees

3D (p-y) SAP2000

2D (p-y) OpenSees

2D (p-y) SAP2000

3D (p-y) Abaqus

3D (p-u) OpenSees

OpenSees

3D Flac SANISAND

OpenSees

3D Flac SANISAND

3D (p-u) OpenSees

*Summary of recent numerical studies on pile foundation in liquefiable soil.*

Wang et al. [131] 2D (p-y)

Zhang et al. [41] 2D (p-y)

3D FEM Shaking

3D DIANA Shaking

**References Analysis** 

Dash et al. [57] 3D (p-y)

Cubrinovski et al. [119]

Cheng and Jeremic´ [120]

McGann et al. [117]

Wang et al. [122]

Valsamis et al. [123]

Bhowmik et al. [124]

Wang and Orense [125]

Sextos et al. [126]

Li and Motamed [128]

Rostami et al. [118]

Zhang et al. [130]

Hamayoon et al. [127]

Lombardi and Bhattacharya [129]

López Jiménez et al. [132]

Kazemi Esfeh and Kaynia [134]

Rajeswari and Sarkar [135]

Rahmani and Pak [121]


*The Dynamic Behaviour of Pile Foundations in Seismically Liquefiable Soils: Failure… DOI: http://dx.doi.org/10.5772/intechopen.94936*

#### **Table 2.**

*Summary of recent numerical studies on pile foundation in liquefiable soil.*

**Figure 10.**

*An example of three numerical modelling of pile in liquefiable of soil [118]. (a) Deformed shape of model of unimproved soil with 3 m thickness of liquefiable soil; (b) pile deformation.*

bridge pile failure in 1964 Niigata earthquake. In this context, McGann et al. [117] proposed a simplified procedure for the analysis of single piles subject to lateral spreading based on a parametric study. Moreover, the values of degradation factors of p-y curves in liquefiable soils computed in 3D FEM using OpenSees [137].

Two-dimensional models have been used to study soil-structure interaction in the majority of the numerical analyses using OpenSees. Haldar and Babu [138] examined the failure mechanism in piles and observed the failure mode was greatly dependent on the depth of the liquefiable soil layer. Zhang and Hutchinson [139] proposed a strategy by integrating the calculated plastic curvature at all integration points along the pile shaft. It was reported that the plastic hinge length of piles extending through liquefiable layers is about 1.4 times larger than that of non-liquefiable conditions. However, the location of plastic hinges can be affected by a variety of factors, such as material properties, pile length and thickness of the liquefied soil layer [118]. Wang and Orense [125] used a 2DBNWF finite element model implemented via Open Sees to analyse the response of raked pile foundations in liquefying ground. Bhowmik et al. [124] investigated the nonlinear behaviour of single hollow pile in layered soil subjected to varying levels of horizontal dynamic load. It found that separation of pile from the surrounding soil considerably affects the resonance frequency and amplitude of the pile foundations. Finn [109] compered different factors that can take into the behaviour of pile foundations during earthquakes in both liquefiable and non-liquefiable soils. Through a 2D nonlinear dynamic finite element (FE) modelling, Li and Motamed [128] presented a large-scale shake table test. It demonstrated that the FE model was able to reproduce the shaking table model behaviour with reasonable accuracy.

Three-dimensional analysis has become more common in the analysis of a full behaviour soil–pile–superstructure system with the greatest potential for accurately and certainly using either solid elements or beam-column elements. Zhang and Liu [140] performed a total of 90 3D finite element analyses using ABAQUS/Explicit to investigate the seismic response of different pile-raft-superstructure systems constructed on soft clay subjected to far-field ground motions. Zhang et al. [130] reported a good agreement between the numerical and the experimental data. Jiménez et al. [132] analysed the effects of this interaction, numerical models with a 3-storey reinforced concrete building using Flac 3D. Esfeh and Kaynia [134] used the software FLAC3D and the SANISAND constitutive model to conduct the nonlinear dynamic analyses for Offshore Wind Turbines. It was found that SANISAND

**199**

**Figure 11.**

*Summary of the most common remediation techniques.*

*The Dynamic Behaviour of Pile Foundations in Seismically Liquefiable Soils: Failure…*

number of numerical simulations with their experimental results.

foundations founded in liquefiable soils are summarised in **Figure 11**.

shaking significantly influenced the effectiveness of drains [148].

Installation of drains (e.g., using stone columns, sand compaction piles, prefabricated vertical drains (PVDs)) can prevent or delay liquefaction by enhancing dissipation of excess pore pressures and preventing void redistribution and the formation of a water lens below a low permeability crust [144–147]. However, deviatoric deformation and volumetric strains due to localised drainage during

A number of densification techniques (e.g., using deep dynamic compaction, vibro-compaction, compaction piles) have been widely studied, because these techniques are relatively simple and practical, and the resulting remediation success can be easily verified by using in-situ penetration techniques [149–152]. However, Rayamajhi et al. [153, 154] reported that the densification and drainage techniques of improvement are often ineffective while the soil-cement columns were relatively

model is capable of simulating the pore pressure generation in the free-field as observed in a recent centrifuge test. Recently, Manzari et al. [141] compered 11 sets of Type-B numerical simulations with the results of a selected set of centrifuge tests conducted in the LEAP- 2017 project. They obtained a good match trends in a

Various ground improvement techniques have been developed for remediation of piled foundations in liquefiable soils over the past few decades. New techniques are introduced either to prevent liquefaction or to minimise the resulting settlements. Piled foundations of existing buildings are often difficult to access for retrofitting and, in addition, any procedure must ensure that the superstructure is not damaged during remediation [142]. Remediation of liquefiable soils for pile foundations needs to meet the several design performances required [143]. First, the most appropriate method for remediation should be selected for a specific portion or area (e.g. ground improvement). Next, the effective of the remedial measure should be appropriately determined to eliminate liquefaction and the associated ground deformations (lateral spreading and settlement). Moreover, the economic viability of the scheme should be evaluated to reduce or avoid potential structural damage caused by liquefied soil. The most common remediation techniques for pile

*DOI: http://dx.doi.org/10.5772/intechopen.94936*

**4. Remediation schemes**

*The Dynamic Behaviour of Pile Foundations in Seismically Liquefiable Soils: Failure… DOI: http://dx.doi.org/10.5772/intechopen.94936*

model is capable of simulating the pore pressure generation in the free-field as observed in a recent centrifuge test. Recently, Manzari et al. [141] compered 11 sets of Type-B numerical simulations with the results of a selected set of centrifuge tests conducted in the LEAP- 2017 project. They obtained a good match trends in a number of numerical simulations with their experimental results.
