EXPERIMENTAL AND NUMERICAL ANALYSIS OF THE … · Figure 2.3 Assumed failure scheme for a...

SCHOOL OF CIVIL, ENVIRONMENTAL AND LAND MANAGEMENT

ENGINEERING

Master’ s degree

In Civil Engineering - Geotechnics

EXPERIMENTAL AND NUMERICAL ANALYSIS

OF THE MECHANICAL RESPONSE OF RIGID PILES

SUBJECTED TO TENSILE LOADS

Advisor

Prof. Ing. Claudio Giulio Di Prisco

Co-Advisor

Prof. Ing. Gabriele Della Vecchia

Candidate

Cristiano Tribulini

ID 877438

Academic Year 2018/2019

EXPERIMENTAL AND NUMERICAL ANALYSIS OF THE MECHANICAL RESPONSE OF RIGID

PILES SUBJECTED TO TENSILE LOADS



Alla mia famiglia



Ringraziamenti

Con questo lavoro di tesi termina la mia carriera universitaria e, di conseguenza,

un’importante fase della mia vita. È stato un percorso non sempre facile, costellato di ansie

e dolori, di sabati sera passati in biblioteca e feste saltate ma, al contempo, anche ricco di

gioie e soddisfazioni, di crescita personale e nuove conoscenze.

Risulta quindi difficile ringraziare in poche righe tutti coloro che, in un modo o nell’ altro,

sono stati artefici di questo mio traguardo.

Innanzitutto, ringrazio il Politecnico di Milano per avermi accolto nel suo ambiente

stimolante, multiculturale e ricco di opportunità e prospettive per il futuro.

La mia gratitudine va poi ai professori, in particolare ai miei relatori, il prof. Claudio Giulio

Di Prisco e il prof. Gabriele Dell Vecchia per ver creduto in me affidandomi questo progetto,

per l’estrema disponibilità e per essersi rivelati dei grandi maestri, sia dal punto di vista

professionale, sia dal punto di vista umano. Ringrazio inoltre l’ing. Gabriele Frigerio per la

pazienza e il sostegno dimostratomi in questi mesi.

Ringrazio di cuore la mia famiglia per essermi stata vicina, sostenendo sempre le mie scelte

e non facendomi mai sentire solo. Grazie ai nonni, a quelli che ci sono e quelli che non ci

sono più, perché grazie alla loro semplicità e al loro affetto ho imparato ad apprezzare

l’importanza delle piccole cose che la vita ci offre.

Grazie a mamma Viviana, a papà Vincenzo e a mia sorella Benedetta per i valori e l’affetto

che mi trasmettono ogni giorno e per il sostegno economico frutto di tanti sacrifici, grazie ai

quali non avrei potuto raggiungere questo traguardo.

Grazie infine ai miei amici, a quelli di Milano per essere diventati la mia nuova famiglia e a

quelli di Piobbico per essere sempre un punto di riferimento della mia vita e per avermi

strappato una risata al telefono anche nei momenti più difficili.

Grazie.



Abstract

Monopile foundations are widely used in offshore and inshore engineering. These

foundations are characterized by a low slenderness ratio. The aim of the present Master thesis

work is to investigate the behaviour of these structures when subjected to tensile and lateral

cyclic loads. In particular, a small-scale laboratory model of a steel monopile foundation in

dry sand was developed, and three different kinds of test were performed: simple pullout

tests, pullout after lateral cyclic load tests and radial tests. The variation of pullout resistance

and lateral displacements were investigated for different horizontal load history (load

amplitude and number of cycles) and different soil conditions (loose and dense sand). The

results of the radial tests have been exploited to draw an interaction domain for monopiles.

Finally, a Finite Element model was developed to reproduce pile behaviour along tensile and

lateral loadings path.



Sommario

I monopali di fondazione sono strutture ampliamente utilizzate nell’ ingegneria off-shore e

in-shore e sono caratterizzate da un basso rapporto di snellezza. Lo scopo di questo lavoro

di tesi magistrale è lo studio del comportamento di queste fondazioni quando sono soggette

a cicli di carico orizzontale e a forze di trazione. In particolare, è stato sviluppato un modello

di laboratorio in piccola scala di un monopalo in acciaio su sabbia e sono state svolte tre tipi

di prove: prove di pullout semplice, prove di pullout dopo cicli di carico orizzontale e prove

radiali. Sono state studiate le variazioni della resistenza allo sfilamento e degli spostamenti

orizzontali, cambiando la storia di carico orizzontale (ampiezza della forza e numero di cicli)

e le condizioni del terreno (sabbia sciolta e densa). Poi, grazie ai risultati dei test radiali è

stato tracciato il dominio di interazione del monopalo. Infine, è stato sviluppato un modello

agli Elementi Finiti per riprodurre la prova di pullout semplice e le prove di carico laterale.



I

Index of contents

Index of contents .................................................................................................................... I

Index of figures .................................................................................................................... III

Index of tables ...................................................................................................................... X

1 INTRODUCTION ......................................................................................................... 1

2 STATE OF THE ART ................................................................................................... 3

2.1 Deep foundations .................................................................................................... 3

2.2 Background history ................................................................................................. 5

2.3 Axial loads .............................................................................................................. 7

2.3.1 Compressive loads ........................................................................................... 7

2.3.2 Tensile load ................................................................................................... 10

2.4 Lateral loads .......................................................................................................... 20

2.4.1 Overview ....................................................................................................... 20

2.4.2 Lateral bearing capacity................................................................................. 21

2.4.3 Lateral displacement ...................................................................................... 26

2.5 Horizontal cyclic loads ......................................................................................... 29

2.6 Inclined loads ........................................................................................................ 38

3 LABORATORY MODEL ........................................................................................... 42

3.1 Experimental apparatus ......................................................................................... 42

3.1.1 The tank ......................................................................................................... 43

3.1.2 The distribution caisson ................................................................................. 44

3.1.3 The box .......................................................................................................... 44

3.1.4 Loading apparatus.......................................................................................... 45

3.1.5 Measurement apparatus ................................................................................. 46



II

3.1.6 Control station ............................................................................................... 47

3.1.7 Calibration ..................................................................................................... 49

3.1.8 The foundation system .................................................................................. 54

3.1.9 Soil used in the investigation ......................................................................... 55

3.2 Installation process ............................................................................................... 60

3.3 Testing program .................................................................................................... 63

3.4 Simple pullout test ................................................................................................ 67

3.4.1 Estimation of interface friction angle ............................................................ 70

3.5 Pull out after lateral cyclic load ............................................................................ 72

3.5.1 Lateral behavior ............................................................................................. 72

3.5.2 Pullout capacity ............................................................................................. 91

3.6 Radial test ............................................................................................................. 97

3.6.1 Interaction domains ....................................................................................... 97

3.6.2 Force-displacement evolution ..................................................................... 101

4 NUMERICAL ANALYSIS ....................................................................................... 103

4.1 The finite element model .................................................................................... 103

4.2 Numerical simple pullout .................................................................................... 105

4.3 Lateral loading test .............................................................................................. 107

5 CONCLUSIONS ....................................................................................................... 111

Appendix A: experimental results ..................................................................................... 113

Simple pullout test ......................................................................................................... 113

Pullout after lateral cyclic load ...................................................................................... 114

Radial tests results ......................................................................................................... 127

References ......................................................................................................................... 129



III

Index of figures

Figure 1.1 Suggested design approach by principal guidelines ............................................ 1

Figure 1.2 Sailing effect on a solar panel .............................................................................. 2

Figure 2.1 Burj Khalifa, Dubai. Whit its 823 m, it is the tallest building of the world. It is

founded on 192 drilled piles .................................................................................................. 4

Figure 2.2 Design of a pile driver machine, Leonardo Da Vinci , Codice Atlantico ............ 5

Figure 2.3 Assumed failure scheme for a vertically loaded pile ........................................... 7

Figure 2.4 Commonly used solutions .................................................................................... 8

Figure 2.5 Transfer curves for driven piles in non-cohesive soil (Reese and O’Neill, 1989)9

Figure 2.6 Assumed failure mechanism for pull-out (Meyerhof, 1973) ............................. 10

Figure 2.7 Force-displacement curve of 2 pile with different diameters (Hanna, 1986) .... 11

Figure 2.8 Ku coefficient trend depending on friction angle (Hanna e Afram, 1986) ........ 12

Figure 2.9 Net uplift capacity for single piles versus relative density of sand .................... 13

Figure 2.10 Net uplift load versus normalized displacement for single piles. L/d=14........ 13

Figure 2.11 Values of 𝑇𝛾 ∙ 𝑑 ∙ 𝐿2 versus normalized displacement ∆𝑑 for single pile ...... 14

Figure 2.12 Schematic view of the experimental apparatus ................................................ 14

Figure 2.13 Load displacement curve for rough vertical and batter piles in dense sand,

L/d=15 and Rd=81% ........................................................................................................... 15

Figure 2.14 Load displacement curve for rough vertical and batter piles in loose sand, L/d=15

and Rd=25% ........................................................................................................................ 15

Figure 2.15 Variation of pullout capacity with pile shape .................................................. 16

Figure 2.16 Variation of pullout capacity of batter pile with pile roughness and sand relative

density, (L/d=15) ................................................................................................................. 16

Figure 2.17 Variation of pullout capacity of batter rough pile with inclination angle and sand

relative density for different slenderness ratio (L/d) ........................................................... 17



IV

Figure 2.18 Variation of pullout capacity with batter angle ................................................ 18

Figure 2.19 Variation of shaft with embedment ratio, (L/d) resistance of vertical and batter

rough Pile ............................................................................................................................. 19

Figure 2.20 Change of the resultant force P as a function of the displacement δ, Viggiani

(1999) .................................................................................................................................. 20

Figure 2.21 Possible failure mechanisms in case of prevented rotation in cohesionless soil

for (a) short pile, (b)intermediate pile) and (c) long pile, Viggiani (1999) ......................... 22

Figure 2.22 Limit values of horizontal force H for intermediate pile prevented to rotate in

cohesionless soil, ................................................................................................................. 24

Figure 2.23 Basic strain wedge in uniform soil ................................................................... 25

Figure 2.24 Deflection pattern of laterally loaded long pile and associated strain wedge .. 25

Figure 2.25 Proposed geometry of compound passive wedge ............................................ 26

Figure 2.26 Principle for describing soil behavior with p-y curves (API, 2000) ................ 27

Figure 2.27 Bending moment diagram for a pile free and prevented to rotate.................... 28

Figure 2.28 Deformed shape diagrams for a pile free and prevented to rotate ................... 28

Figure 2.29 Degradation of stiffness after number of cycles .............................................. 29

Figure 2.30 Lateral displacement of monopiles under static lateral load with regard to

normalized load ................................................................................................................... 32

Figure 2.31Comparison of clamping effect for piles with different diameters:(a) D=7.5m (b)

D=2.5m ................................................................................................................................ 33

Figure 2.32 Effect of embedded length on the accumulation rate after 100 cycles for a

monopile with D=5m, Tp=0.09m, H=5MN and h=20m ..................................................... 33

Figure 2.33 Effect of pile diameter on the accumulated rate after 100 cycles for a monopile

with L=20m, Tp=0.09m, H=10MN and h=4m .................................................................... 33

Figure 2.34 Method for determination of stiffness and accumulated rotation: (a) cyclic test;

(b) static test ........................................................................................................................ 34



V

Figure 2.35 Measured displacements as a function of N, Rd, 𝜉𝑏 and 𝜉𝑐. Dotted lines are

obtained by using equation 2.28 .......................................................................................... 35

Figure 2.37 Images of the small (D=0.273m), medium (D=0.726m) and large (D=2m)

diameter test arrangements .................................................................................................. 36

Figure 2.36 Field pile load test procedure ........................................................................... 36

Figure 2.38 Comparison of ground level load-displacement response for L/D=5.25 and

D=0.726m ............................................................................................................................ 37

Figure 2.39 Radial displacements tests in the H-V plane .................................................... 38

Figure 2.40 Selected load paths from numerical radial displacement test (a), load paths from

numerical swipe test (b), numerical swipe tests with more complex load paths (c) and

complete results from numerical radial displacement test (d), in H-V plane (M=0) .......... 39

Figure 2.41 Comparison of equation 2.29 with the numerical results (a) in the H-V plane and

(b) in the normalized space .................................................................................................. 40

Figure 2.42 Problem model ................................................................................................. 40

Figure 2.43 Uplift capacity versus length of the pile (L) for D=0.3m ................................ 41

Figure 3.1 Main body of the apparatus ................................................................................ 42

Figure 3.2 Tank lateral view ................................................................................................ 43

Figure 3.3 Grids ................................................................................................................... 43

Figure 3.4 The distribution caisson ..................................................................................... 44

Figure 3.5 The box .............................................................................................................. 44

Figure 3.6 Loading apparatus: (a), the horizontal piston, (b) the cart with the vertical piston

............................................................................................................................................. 45

Figure 3.7 Load cells: (a) horizontal, (b) vertical ................................................................ 46

Figure 3.8 (a) Vertical and (b) horizontal transducers ........................................................ 47

Figure 3.9 Software display ................................................................................................. 48

Figure 3.10 Power station for measuring instruments ......................................................... 48

Figure 3.11 Pressure control panel ...................................................................................... 49



VI

Figure 3.12 Micrometer ....................................................................................................... 50

Figure 3.13 Horizontal transducer calibration ..................................................................... 50

Figure 3.14 Vertical transducer calibration ......................................................................... 51

Figure 3.15 Metal structure adopted to calibrate load cells ................................................. 51

Figure 3.16 Vertical cell calibration .................................................................................... 52

Figure 3.17 Horizontal cell calibration ................................................................................ 52

Figure 3.18 Horizontal pressure cell calibration ................................................................. 53

Figure 3.19 Vertical pressure cell calibration ...................................................................... 53

Figure 3.20 Pile model ........................................................................................................ 54

Figure 3.21 The sleeve......................................................................................................... 55

Figure 3.22 Granulometric curve of Ticino sand ................................................................ 55

Figure 3.23 The pycnometer placed inside the box ............................................................. 58

Figure 3.24 Installed metal guides ....................................................................................... 60

Figure 3.25 The iron mallet inside the tube ......................................................................... 61

Figure 3.26 Flat steel bar and smaller pile installed in the head of the embedded pile ....... 61

Figure 3.27 Final display of the apparatus before the application of load patterns ............. 62

Figure 3.28 Simple pull out load pattern ............................................................................. 63

Figure 3.29 Pull-out after lateral cyclic load patterns ......................................................... 63

Figure 3.30 Radial test load patterns ................................................................................... 64

Figure 3.31Simple pullout test for the driven pile ............................................................... 67

Figure 3.32 Simple pullout test for driven and pre-installed pile for loose and dense sand 69

Figure 3.33 Monotonic lateral load for 1HA30 test in loose and dense sand...................... 72

Figure 3.34 Monotonic lateral load for 1HA200 test in loose and dense sand.................... 73

Figure 3.35 Displacement field around a long pile ............................................................. 74

Figure 3.36 Failure mechanisms of a pile as a function of z/D .......................................... 74



VII

Figure 3.37 Variation of Nq with z/D and friction angle .................................................... 75

Figure 3.38 Sheet pile failure mechanism ........................................................................... 76

Figure 3.39 Lateral pressure coefficients trends .................................................................. 77

Figure 3.40 , The three different phases during lateral loading. .......................................... 78

Figure 3.41 1HA400 test for pre-installed pile .................................................................... 79

Figure 3.42 1HA500 tests in dense and loose sand compared with the other monotonic tests

............................................................................................................................................. 79

Figure 3.43 Shake down response of the system, di Prisco (2012) ..................................... 80

Figure 3.44 Plastic ideal adaptation response, di Prisco (2012) .......................................... 81

Figure 3.45 (a) Constant velocity ratcheting, (b) progressive stabilization, (c) increment

accumulation, di Prisco (2012) ............................................................................................ 81

Figure 3.46 12HA500 test for dense sand ........................................................................... 82

Figure 3.47 Relative displacement between two consecutive cycles (Giannakos, Gazetas,

2002) .................................................................................................................................... 83

Figure 3.48 Relative displacement ∆𝑦𝑁𝑦1 as a function of the number of cycles for driven

pile in loose sand ................................................................................................................. 83

Figure 3.49 Relative displacement ∆𝑦𝑁𝑦1 as a function of the number of cycles for driven

pile in dense sand ................................................................................................................. 84

Figure 3.50 Relative displacement ∆𝑦𝑁𝑦1 as a function of the number of cycles for pre-

installed pile in loose sand ................................................................................................... 84

Figure 3.51 Relative displacement ∆𝑦𝑁𝑦1 as a function of the number of cycles for pre-

installed pile in dense sand ................................................................................................. 85

Figure 3.52 Irreversible displacement (Giannakos, Gazetas, 2012) .................................... 85

Figure 3.53 Irreversible displacements for driven pile in loose sand .................................. 86

Figure 3.54 Irreversible displacements for driven pile in dense sand ................................. 86

Figure 3.55 Irreversible displacements for pre-installed pile in loose sand ........................ 87

Figure 3.56 Irreversible displacements for pre-installed pile in dense sand ....................... 87



VIII

Figure 3.57 Stiffness for different load cycles (Giannakos, Gazetas 2012) ........................ 88

Figure 3.58 Variation of secant stiffness with number of cycles for driven pile in loose sand

............................................................................................................................................. 89

Figure 3.59 Variation of secant stiffness with the number of cycles for driven pile in dense

sand ...................................................................................................................................... 89

Figure 3.60 Variation of secant stiffness with number of cycles for pre-installed pile in loose

sand ...................................................................................................................................... 90

Figure 3.61 Variation of secant stiffness with number of cycles for pre-installed pile in dense

sand ...................................................................................................................................... 90

Figure 3.62 Pullout resistance for driven pile in loose sand as a function of horizontal force

............................................................................................................................................. 91

Figure 3.63 Pullout resistance for driven pile in dense sand as a function of horizontal force

............................................................................................................................................. 92

Figure 3.64 Pullout resistance for pre-installed pile in dense sand as a function of horizontal

force ..................................................................................................................................... 92

Figure 3.65 Pullout resistance for 200 N test in loose and dense sand................................ 93

Figure 3.66 Pullout resistance for pre-installed pile in loose sand as a function of horizontal

force ..................................................................................................................................... 93

Figure 3.67 Pullout force as a function of the number of cycles for a maximum horizontal

load of 30 N ......................................................................................................................... 94


load of 40 N ......................................................................................................................... 94


load of 50 N ......................................................................................................................... 95


load of 100 N ....................................................................................................................... 95


load of 300 N ....................................................................................................................... 96



IX

Figure 3.72 Pull out force as a function of the number of cycles for a maximum horizontal

load of 200 N ....................................................................................................................... 96

Figure 3.73 Failure domain for driven pile in loose sand .................................................... 99

Figure 3.74 Failure domain for pre-installed pile in loose sand .......................................... 99

Figure 3.75 Interaction domain for driven pile in loose sand ............................................ 100

Figure 3.76 Pull out for radial tests in driven pile ............................................................. 102

Figure 3.77 Role of horizontal load in concave and convex domains .............................. 102

Figure 4.1 Geometry and mesh discretization ................................................................... 104

Figure 4.2 Numerical simple pull out test ......................................................................... 106

Figure 4.3 Comparison between numerical and experimental pull out ............................. 106

Figure 4.4 Comparison between numerical and empirical results for 1HA200 test.......... 107

Figure 4.5 Values of displacement for 200N horizontal load along x direction [mm]...... 108

Figure 4.6 Total displacement of the soil .......................................................................... 108

Figure 4.7 Maximum soil stress for 200N horizontal load along x direction, [N/mm2] ... 109

Figure 4.8 Expansion and compression thrust trends ........................................................ 110



X

Index of tables

Table 3.1 Pile features ......................................................................................................... 54

Table 3.2 sand features ........................................................................................................ 56

Table 3.3Relative density computation ............................................................................... 59

Table 3.4 Performed pull out tests ....................................................................................... 65

Table 3.5 Performed pull out tests after lateral cyclic loading in loose sand ...................... 65

Table 3.6 Performed pull out tests after lateral cyclic loading in dense sand ..................... 66

Table 3.7 Performed tensile radial tests in loose sand ......................................................... 66

Table 3.8 Performed compression radial test for driven pile in loose sand........................ 67

Table 3.9 Pullout forces for driven and pre-installed piles.................................................. 69

Table 3.10 Radial pullout forces for driven pile in loose sand ............................................ 97

Table 3.11 Radial pullout forces for pre-installed pile in loose sand .................................. 98



INTRODUCTION 1

1 INTRODUCTION

Monopiles are a particular kind of deep foundations characterized by a low slenderness ratio

L/D<10, where L denotes the length of the pile and D its diameter. They are commonly made

in steel and they are employed for solar panels and off-shore wind turbines.

Nowadays, studies and experimental evidences of cyclic and pullout solicitations on this

kind of piles are few and fragmented so that it is difficult to get an overall picture of the

general performances of these structures subjected to these loads. Anyway, today’ s focus

on renewable energy sources as a replacement for fossil fuels has made the off-shore and

solar industries expand rapidly. So, the present-day field of application of these

acknowledgments suggests that in the next few years the study of this kind of deep

foundation will be a central issue for the industry and the geotechnical academic world.

The current principal design guides suggest designing these foundations with the aid of

simplified analysis approaches (Figure 1.1), such as p-y curves, and considering cycles effect

with a reduction coefficient. However, large wind turbine farms and solar plants still

increasing in size are continuously installed in rough environments where waves and

windstorms continuously hit them, modifying the tensional state of the soil. So, the effect of

long-term cyclic loading on monopiles is a critical design factor and the effect of change in

load characteristics, soil parameters and number of load cycles should be properly examined.

Figure 1.1 Suggested design approach by principal guidelines



INTRODUCTION 2

The aim of the present work is to investigate the behaviour of a monopile foundation in

granular soil subjected to pullout and lateral cyclic loads. In particular, it was investigated

how the horizontal load history affects the pullout capacity of the pile.

For this purpose, a small-scale laboratory model of a steel driven monopile foundation in

sand was developed. Laboratory tests were conducted with different soil conditions (loose

and dense sand) and with different load characteristics. There were performed test under

simple pullout load, under pullout load after asymmetric cyclic lateral loads and under radial

conditions.

In this way it was possible to reproduce, for example, the real case of a monopile foundation

for solar panel continuously hit by windstorms. Due to the inclination of the panel, horizontal

wind forces are also converted in tensile forces for the structure in the so called “sailing

effect” as depicted in figure 1.2.

Results were then compared with the one obtained by a Finite Element model developed

with Midas Gts NX software.

This thesis encompasses 6 chapters. Chapter 2 is a brief overview of deep foundations and

the state of the art. Chapter 3 on the other hand, introduces the adopted small-scale model.

the laboratory devices, the calibrations, the testing procedures and the testing program. The

second part of the chapter showcases the tests results and presents a discussion of them,

mainly focusing on comparing the effects of sand density and load history. The penultimate

chapter compares the experimental study with the numerical results obtained from the FE

software. Finally, chapter 5 is a synopsis of the work carried out in this thesis and includes

some remarks on the knowledge gap and the need for future research.

Figure 1.2 Sailing effect on a solar panel



STATE OF THE ART 3

2 STATE OF THE ART

The first part of the chapter presents a brief introduction on deep foundations and some

historical remarks. Then, from chapter 2.3, it is presented a literature review about the state

of the art of piles subjected to axial, lateral, cyclic and inclined loads

2.1 Deep foundations

Deep foundations go unseen by the majority of our population but make the modern world

possible. Such structural elements are employed for a large assortment of constructions: from

buildings to roadways and railways to the iconic skyscrapers of the largest metropolis of the

world (figure 2.1).

A deep foundation is a structure that transfers surface loads to lower level in the soil mass.

The most common reasons to employ deep foundations are very large design loads (such as

those associated with a skyscraper), poor shallow soils which are unsuitable for construction

and site constraints like property lines or neighboring structures.

The bearing capacity of the foundation may be due to three different mechanisms:

• base resistance: the foundation base reaches a soil stratum where the geologic

material has a greater bearing capacity (usually bedrock).

• shaft resistance: the foundation takes advantage of the skin friction between its lateral

surface and the surrounding soil.

• mixed resistance: the foundation exploits both base and lateral resistance

https://en.wikipedia.org/wiki/Property_line



STATE OF THE ART 4

The most common type of deep foundation is the pile, a column of timber, steel or concrete

installed within the ground, whose external diameter is much smaller than its length. Piers

and monopile are other types of deep foundations which have much larger diameter

compared to their length and they are typically used for offshore structures.

Piles can be classified on their method of installation. Bored piles involve the soil removal

by boring or drilling to form a shaft, and then concrete is cast in the shaft to form the pile.

Displacement piles are driven in the soil via impact of piling hammer, vibration or mixed

techniques that produce disturbance of the soil around the pile. In particular, in coarse soil

the piling procedure increase the density of the soil near the pile, improving its mechanical

characteristics. In cohesive soil, the piling process can be divided into two stages. The first

one is the piling stage, where, due to undrained conditions, the pore water pressure built up

causes a reduction of the normal effective stress on the interface which help the piling

procedure. Then, the consolidation stage occurs, and the horizontal stress takes values equal

or higher than the initial one. This causes a reduction of void ratio and an improvement of

the mechanical characteristics of the soil.

It follows that the installation technique, the pile shape and the soil type play a key role on

the design of piles.

Figure 2.1 Burj Khalifa, Dubai. Whit its 823 m, it is the tallest building of the world. It is founded on 192 drilled piles



STATE OF THE ART 5

2.2 Background history

In ancient times, people settled in river valleys on weak soils, peats, and on flood-prone

sections. The weak bearing ground was reinforced using timber piles that were either

manually forced into the ground or fixed in holes that were filled with stones and sand. The

use of wooden piles as foundations allowed to build homes above water level, avoiding

floods, enemies and predators. This had a key role on the development of trade and the birth

of civilization.

Pile technology was then extremely developed in ancient Rome. One need only think the

term "pilium" in a literal transcription means a "heavy legionnaire's lance." Military

formations, which constructed buildings, roads, and bridges across rivers moved throughout

Europe after wars-conquerors and spread this technology all over the ancient world. Time

has confirmed the reliability and longevity of the foundations built from piles by ancient

Roman builders in all the different soil regions of Europe, Asia, and Africa.

The most ancient sources of information on foundation engineering are the recommendations

of Vitruvia and detailed descriptions of bridge construction compiled by Caesar.

After the fall of the Roman empire the technology was still largely employed and refined by

engineers and architects by the likes of Leonardo Da Vinci (figure 2.2) but no significant

improvements were developed up to the 19th century.

Figure 2.2 Design of a pile driver machine, Leonardo Da Vinci , Codice Atlantico



STATE OF THE ART 6

Industrial revolution marked a turning point on the construction of piles thanks to

technological advancements, metallurgic innovations and the large-scale production of

Portland cement. Lots of constructors started to study the behavior of piles and their bearing

capacity. There were developed new types of piles and new installation methods. This led to

make these structures more suitable to be installed in difficult environments and to sustain

higher and higher loads.

Due to the intensive use of these structural elements for over a century, it follows that there

exists an incredible amount of empirical and literature studies about the bearing capacity of

piles subjected to compressive loads coming from the overall structures. On the contrary the

study of the uplift capacity was not investigated since no practical applications were needed.

.



STATE OF THE ART 7

2.3 Axial loads

2.3.1 Compressive loads

According to NTC2008 it is possible to evaluate the bearing capacity through an analysis of

the failure of the pile-soil system (static relationship): pile is assumed to be a rigid body and

soil as a rigid perfectly plastic medium. The problem is similar to the one used for shallow

foundation, but the issue is more complex (axis-symmetric geometry, greater depths,

influence of the mechanical characteristics of the soil-pile interface).

The assumed scheme of failure is shown in figure 2.3.

Imposing the vertical equilibrium:

𝑄𝐿𝐼𝑀 + 𝑊𝑃 = 𝑄𝑃 + 𝑄𝑆 (2.1)

Where

𝑊𝑃 is the pile weight.

𝑄𝑃 is the base resistance

𝑄𝑆 is the shaft resistance

Figure 2.3 Assumed failure scheme for a vertically loaded pile



STATE OF THE ART 8

It is possible to obtain the maximum bearing capacity 𝑄𝐿𝐼𝑀 of the pile just simply adding the

maximum mobilized values of 𝑄𝐵 and 𝑄𝑆 obtained through static formulas:

𝑄𝐿𝐼𝑀 = 𝑄𝐵 + 𝑄𝑆 − 𝑊𝑃 (2.2)

For coarse grained soils:

• the base resistance is determined analytically by treating the pile as a very deeply

embedded shallow foundation.

The base resistance

𝑄𝐵 = 𝑞𝑏𝐴𝑏 = 𝑁𝑞𝜎𝑣𝑜′ 𝐴𝑏 (2.3)

Where 𝐴𝑏 is the base area of the pile, 𝜎𝑣𝑜′ the effective vertical stress on the tip and

𝑁𝑞 a coefficient depending on soil friction angle, shape, relative depth of the

foundation and the considered failure mechanism as shown in figure 2.4.

• the shaft resistance is obtained through the so called “β method”

𝑄𝑆 = ∫ 𝑓𝑠 ∙ 𝜋 ∙ 𝐷 ∙ 𝑑𝑧

𝐿

0

(2.4)

Figure 2.4 Commonly used solutions



STATE OF THE ART 9

Where D is the pile diameter and 𝑓𝑠 is the shaft resistance at depth z at the interface

between the pile and the sand

𝑓𝑠 = 𝛽𝜎𝑣𝑜′ = 𝐾𝜎𝑣𝑜

′ 𝑡𝑎𝑛𝛿 (2.5)

Where K is the thrust coefficient of the soil and 𝛿 the interface friction angle

So, at the end it is possible to write

𝑄𝐿𝐼𝑀 = 𝑞𝑏 ∙ 𝐴𝑏 + ∫ 𝑓𝑠 ∙ 𝜋 ∙ 𝐷 ∙ 𝑑𝑧

𝐿

0

− 𝑊𝑃 (2.6)

It is worth noting that the simple additivity between 𝑄𝐵 and 𝑄𝑆 is an assumption: lateral and

tip stresses are mobilized following different rules. It is possible that, at failure, they do not

reach their maximum value.

In fact, as soon as 𝑄𝐿𝐼𝑀 is applied, it is resisted just by 𝑄𝑆 on the top part of the pile.

Increasing the applied load, also 𝑄𝑆 increases and moves downward. At a certain point also

the base starts to move and compression stresses 𝑞𝑏 arises on the pile tip. Then 𝑄𝑆 stops to

increase and 𝑄𝐵 increases up to ultimate equilibrium conditions.

From the practical point of view, it is possible to say that the complete mobilization of the

lateral resistance 𝑄𝑆 happens when the ratio between settlements and pile diameter D is 𝑠

𝐷≅

0.5% while the base resistance 𝑄𝐵 reaches the maximum mobilization for 𝑠

𝐷 values much

higher than 10% as noted in figure 2.5.

Figure 2.5 Transfer curves for driven piles in non-cohesive soil (Reese and O’Neill, 1989)



STATE OF THE ART 10

2.3.2 Tensile load

The pullout capacity of batter pile in sand has been the subject of few studies that show a

wide discrepancy among them.

Some studies have concluded that shaft resistance is about the same for uplift and

compression loads. However, O’Neill and Reese (1999) reported that the shaft resistance in

tension could be 12–25% smaller than in compression due to Poisson’s ratio effects, which

would tend to reduce the shaft diameter in uplift. Poulos and Davis (1980) recommended

estimating the uplift capacity of piles as 2/3 of the downward shaft resistance. The vertical

pull-out resistance 𝑃𝑢 of a foundation pile in sand can be expressed as a function of the lateral

resistance 𝑃0 and the pile’s weight 𝑊𝑃

𝑃𝑢 = 𝑃0 + 𝑊𝑃 (2.7)

Meyerhof and Adams (1968) proposed a theory regarding the uplift capacity of shallow

foundations. Then, Meyerhof (1973) extended this theory to pile foundations assuming that

failure surface was on the pile vertical wall, as shown in figure 2.6

Figure 2.6 Assumed failure mechanism for pull-out (Meyerhof, 1973)

the equation (2.7) can be rewritten as

𝑃𝑢 = 𝜋𝐷𝑃𝑃 sin 𝛿 + 𝑊𝑃 (2.8)

Where 𝑃𝑃 is the total passive force acting on the pile’s wall and D is pile diameter.

Furthermore, according to figure 2.6 it is possible to write:



STATE OF THE ART 11

𝑃𝑃 cos 𝛿 = 𝛾𝐾𝑃 (

𝐿2

2)

(2.9)

Where 𝐾𝑃 is the coefficient of passive thrust, L is the pile’s length and 𝛾 the specific

weight of the soil.

Combining equations (2.8) and (2.9) it follows:

𝑃𝑢 = 𝜋𝐷𝛾𝐾𝑃 (

𝐿2

2) 𝑡𝑎𝑛𝛿 + 𝑊𝑃

(2.10)

It is possible to define the uplift coefficient as

𝐾𝑢 = 𝐾𝑃𝑡𝑎𝑛𝛿 (2.11)

In order to define the pull-out resistance as

𝑃𝑢 = 𝜋𝐷𝛾𝐾𝑢 (

𝐿2

2) + 𝑊𝑃

(2.12)

Hanna and Hafram (1986) performed a series of experimental pullout tests on single piles

in sand with different diameters (figure 2.7).

The uplift coefficient was then back-calculated using test results (figure 2.8).

Figure 2.7 Force-displacement curve of 2 pile with different diameters (Hanna, 1986)



STATE OF THE ART 12

2.3.2.1 Influence factors for uplift capacity

The pull-out resistance of a single pile depends on several factors as the material type, the

relative density, the inclination of the pile with respect to the ground surface, the load

inclination and the shape of the pile.

Gaaver K.E., 2013 performed several tests changing the embedment depth-to-diameter

ratios (L/d = 14, 20 and 26), relative density of sand (Dr = 75%, 85% and 95%) and the

number of piles (1,2,4 and 6).

Figure 2.9 shows that for a particular upward displacement, the magnitude of the net uplift

load of a single pile improves with an increase in the relative density of sand. This can be

attributed to the increase in both the effective stress and the friction angle between pile and

soil due to the increase in the relative density of soil. The net uplift capacity of a pile

increases by a factor of 1.37 as a result of increasing the sand relative density from 75% to

85%, and the increase in relative density from 85% to 95% improves the net uplift capacity

by a factor of 1.18. Figure 2.10 illustrates the effect of relative density on the uplift capacity

of single piles at different (L/d) ratios. As previously mentioned, the increase in the relative

density appreciably improves the net uplift capacity for all values of (L/d). Therefore, it can

be concluded that the relative density of soil has a significant contribution to both the net

uplift capacity and the displacement at the uplift capacity of single piles. Figure 2.10 also

shows that the pile embedment depth has a major influence on the net uplift capacity of

Figure 2.8 Ku coefficient trend depending on friction angle (Hanna e Afram, 1986)



STATE OF THE ART 13

single piles. It can be clearly observed that for a particular relative density, the net uplift

capacity increases significantly with an increase of (L/d) ratio. This effect can be attributed

to two different factors. The first one is the improvement in the friction resistance between

the soil and the pile. As the pile embedment depth increases, the effective stress at the mid-

height of the pile increases, and consequently, an improvement in the shear resistance is

achieved. The second factor is the increased contact area between the soil and the pile as the

pile embedment depth L increases. These two factors lead to the improvement in the net

uplift capacity offered by the pile as the pile embedment depth increases. In this situation, it

is important to note that the pile embedment depth in offshore structures should be measured

from the scour level to the tip level of the pile. In other words, the capacity loss due to scour

should not be included in the determination of the axial uplift capacity. In addition,

settlement induced down drag should not be included because they will cease at some point

in time.

Figure 2.10 Net uplift load versus normalized displacement for single piles. L/d=14

Figure 2.9 Net uplift capacity for single piles versus relative density of sand



STATE OF THE ART 14

A general load-displacement relationship was then found between the normalized uplift

load (𝑇

𝛾∙ 𝑑 ∙ 𝐿2) and the normalized upward displacement (

∆

𝑑) as shown in figure 2.11.

(

𝑇

𝛾∙ 𝑑 ∙ 𝐿2) = 24.1 (

∆

𝑑)

0.84

(2.13)

Nazir A. e Nasr A. (2013) performed several tests on model steel piles (figure 2.12) with

smooth and rough surfaces installed in loose, medium, and dense sand with an embedded

depth ratio, L/d, varying from 7.5 to 30 and with different batter angles of 0°, 10°, 20°, and

30°.

In dense sand the maximum value of pullout capacity Pu for rough piles occurs at batter

angle approximately equal to 20° and then decreases as the batter angle continue to increase

as depicted in figure 2.13

Figure 2.11 Values of (𝑇

𝛾∙ 𝑑 ∙ 𝐿2) versus normalized displacement

∆

𝑑 for single pile

Figure 2.12 Schematic view of the experimental apparatus



STATE OF THE ART 15

While, the ultimate pullout capacity of batter rough pile in loose sand (figure 2.14) decreases

with the increase of batter angle. It is also observed a linear relationship in the early stages

of the loading up to normalized displacement of about 1.2%. Afterwards they are non-linear.

Comparing results shown in figures 2.13 and 2.14, it is found that there is a big difference

between the pullout load of dense sand and loose sand, this observation is due to the angle

of internal friction between pile and sand, 𝛿, that influences the coefficient of earth pressure

Ks. For smooth shaft when 𝛿 is much smaller than the angle of internal friction of sand there

is a slight increase of Ks. But in the case of rough piles, where the value of 𝛿 is close to or

equal to the angle of internal friction, Ks significantly increases.

Another investigated aspect was the influence of pile shape. Circular, square and rectangular

pile shapes with an almost equal perimeter were tested in order to study their effect on the

pullout resistance.

Figure 2.14 Load displacement curve for rough vertical and batter piles in loose sand, L/d=15 and Rd=25%

Figure 2.13 Load displacement curve for rough vertical and batter piles in dense sand, L/d=15 and Rd=81%



STATE OF THE ART 16

Figure 2.15 shows a significant effect of pile shape on the pullout resistance of vertical piles

when the value of S/d exceeds 2%. Furthermore, circular piles are more resistant than square

and rectangular piles.

The difference in pile capacities is attributed to the change in radial stress around the pile

perimeter for the different pile shapes which have significant effect in the earth pressure.

The round shape pile has smaller head deformation than the square and rectangular shape of

pile at the same load intensity. There is no appreciable effect of the pile shape on the value

of relative displacement at failure load.

Moreover, the influence of roughness and sand density was analyzed through the relation

between the inclination angle and the pullout capacity of rough and smooth pile, Pu rough and

Pu smooth expressed in non-dimensional form in term of ratio (Pu rough / Pu smooth).

In figure 2.16 it is possible to observe that inclination angle α has a negligible effect while

the increase of sand density causes a decrease of the ratio of (Pu rough/Pu smooth).

Then, it was also studied the influence of pile slenderness ratio as a function of relative

density.

Figure 2.15 Variation of pullout capacity with pile shape

Figure 2.16 Variation of pullout capacity of batter pile with pile roughness and sand relative density, (L/d=15)



STATE OF THE ART 17

It can be pointed out from figure 2.17 that the ultimate pullout capacity increases with the

increase of the slenderness ratio for the pile installed in loose, medium and dense sand.

Furthermore, sand density has significant effect on the pullout capacity of the pile installed

either vertical or inclined. Finally, the rate of increase in pullout capacity increases with the

increase of sand density.

Concerning the inclination angle, twelve series of tests using rough piles installed both

vertical and inclined in loose, medium and dense sand with variable embedment ratios (L/d)

of 7.5, 15, 22.5 and 30 were carried out. Figure 2.18 depicts the ratio between the ultimate

uplift capacity for inclined pile Pa and vertical pile Pv as a function of batter angle.

In dense or medium density sand the ratio Pa/Pv increases with the increase of batter angle

up to a maximum value of 20°. While the increase of the batter angle more than 20° causes

a significant reduction for this value. This behavior is attributed to the dilation that occurs

when dense sand is subjected to shear stress causing an increase in the earth pressure.

For loose sand condition, the increase of the inclination angle causes a reduction in (Pa/Pv)%

for all embedment ratios. Significant reduction is obtained for shallow embedment ratio,

L/d= 7.50. This imply that a kind of relaxation takes place into the soil when the pile is

subjected to uplift forces. This can be explained by the fact that during uplift, the soil moves

upwards with the pile. Accordingly, the earth pressure reduces from a higher value to a lower

one such that the earth pressure reached at limit is lower than the in-situ earth pressure.

Figure 2.17 Variation of pullout capacity of batter rough pile with inclination angle and sand relative density for different

slenderness ratio (L/d)



STATE OF THE ART 18

Finally, the variation of the uplift skin coefficient Ku from the back-calculation of the

experimental results was plotted as a function of batter angle, relative density of sand and

slenderness ratio (L/d). As shown in figure 2.19, the shaft resistance increases with the

increase of embedment ratio. This is due to the increment of the overburden pressure with

the embedment depth. The latter is responsible of generating the horizontal earth pressure

that act as normal stress on the pile shaft. At a certain depth which is defined as the critical

depth (L/d critical), the rate of increase in shaft resistance starts to decrease or to maintain a

constant value. The critical depth is found to be about 14, 16 and 25 for loose, medium and

dense condition respectively.

Figure 2.18 Variation of pullout capacity with batter angle



STATE OF THE ART 19

Figure 2.19 Variation of shaft with embedment ratio, (L/d) resistance of vertical and batter rough Pile



STATE OF THE ART 20

2.4 Lateral loads

The analysis of a deep foundation subjected to a lateral load is a difficult soil-pile interaction

problem. It follows that usually numerical tools are used in order to solve this problem.

2.4.1 Overview

Consider a circular pile embedded in a homogeneous medium. First, the acting normal

tensions on the surface of the pile show an axisymmetric distribution with 0 resultant. Then,

if a horizontal displacement is applied to the pile, the resultant forces change because also

tangential forces arise. (figure 2.20)

It is possible to define P the resultant force on the direction of pile displacement but in

opposite sense. It depends both on the amplitude of the applied displacement and the

reference depth. Usually long pile displacements are confined in their top portion.

Figure 2.20 Change of the resultant force P as a function of the displacement δ, Viggiani (1999)



STATE OF THE ART 21

2.4.2 Lateral bearing capacity

Among the numerous analytical literature solutions, just two representative solution are

presented: the solution by Broms and the 3D strain wedge method.

2.4.2.1 Analytical solution by Broms

Some authors like Brinch-Hansen (1961), Reese et al. (1974) and Broms (1964) tried to find

an analytical solution that allows to get a good approximation of the lateral bearing capacity

of the pile.

For instance, hypothesis made by Broms (1964) were:

• Homogeneous soil with constant properties along depth;

• Rigid-perfectly plastic interface behavior between soil and pile. The soil resistance

is mobilized for every increment of displacement different from 0 and then it remains

constant as displacement increases.

• The resultant of the reaction force P does not depend on the transversal section of the

pile, but only on its diameter;

• Rigid perfectly-plastic flexional behavior of the pile. Elastic rotations of the pile are

negligible as the bending moment reaches its plasticization value My. At this point a

plastic hinge will create and rotation will continue in a non-defined way and with

constant bending moment.

Based on theoretical and experimental analysis, expressions for the computation of the soil

resistance P were formulated. Different analyses were performed in order to take into

account different soil types (cohesive or granular) and different constraints (pile head

constrained or free to rotate).

With reference to the case that will be analyzed in this work, just the pile in granular soil

with no head rotation will be presented. In these conditions, three different possible

mechanisms can happen for short, intermediate and long piles.



STATE OF THE ART 22

In short piles, failure takes place when the applied lateral load is equal to the ultimate lateral

resistance of the soil, and the pile moves as a unit through the soil. The corresponding

assumed distributions of lateral earth pressures and bending moments are shown in figure

2.21(a). A simple horizontal equilibrium equation gives

𝐻 = 1.5 ∙ 𝐿2 ∙ 𝑘𝑝 ∙ 𝛾 ∙ 𝑑 (2.14)

From which

𝐻

𝑘𝑝 ∙ 𝛾 ∙ 𝑑3= 1.5 ∙ (

𝐿

𝑑)

2

(2.15)

Figure 2.21 Possible failure mechanisms in case of prevented rotation in cohesionless soil for (a) short pile, (b)intermediate

pile) and (c) long pile, Viggiani (1999)



STATE OF THE ART 23

H depends only on soil resistance (γ, 𝑘𝑝) and pile embedment ratio (𝐿

𝑑). But first, it is

necessary to verify whether the assumed failure mechanism (short pile) happens. In other

words, it is necessary to check that the maximum bending moment Mmax is smaller than the

plasticization moment My. The maximum bending moment is:

𝑀𝑚𝑎𝑥 =

2

3𝐻𝐿 (2.16)

From which is possible to obtain:

𝑀𝑚𝑎𝑥

𝑘𝑃𝛾𝑑4= (

𝐿

𝑑)

3

(2.17)

For intermediate pile, a rotation of the pile around a point located near pile’s head occurs

with the formation of a plastic hinge as shown in figure 2.21(b). Imposing the horizontal

translational equilibrium, it is obtained:

𝐹 =

3

2𝐿2𝑘𝑝𝛾𝑑 − 𝐻 (2.18)

Considering equation 2.18 and imposing the rotational equilibrium around the plastic hinge:

𝑀𝑦 +

1

2𝐿3𝑘𝑝𝛾𝑑 − 𝐻𝐿 = 0 (2.19)

And so:

𝐻

𝑘𝑃𝛾𝑑3=

1

2∙ (

𝐿

𝑑)

2

+ 𝑀𝑦

𝑘𝑃𝛾𝑑4∙

𝑑

𝐿 (2.20)

In this case it can be noticed that H is a function also of 𝑀𝑦 in addition to γ, 𝑘𝑝 and (𝐿

𝑑).

For long pile mechanism two plastic hinges are formed, one at a certain depth and one near

the pile’ s head. The maximum bending moment along the pile reaches the plasticization

moment 𝑀𝑦 and so a second plastic hinge arises. The rotational equilibrium of the section

of pile between the two plastic hinges gives:

2

3𝐻𝑓 = 2𝑀𝑦 (2.21)

Where 𝑓 is the depth at which the shear stress nullifies and so the bending moment is

maximum. It can be found imposing the shear stress equal to 0.



STATE OF THE ART 24

𝑇 = 𝐻 −

3

2𝑘𝑝𝛾𝑑𝑧2 = 0 (2.22)

And so

𝑓 = 0.816√𝐻

𝑘𝑝𝛾𝑑 (2.23)

Combining equations (2.21) and (2.23) it is obtained

𝐻

𝑘𝑝𝛾𝑑3= √(3.676

𝑀𝑦

𝑘𝑝𝛾𝑑4)

3

(2.24)

Also in this case H depends on 𝑀𝑦 in addition to γ, 𝑘𝑝 and (𝐿

𝑑).

It can be also noticed that L does not appear explicitly but should be extrapolated as the

minimum limit value on the right of the curves for intermediate piles as the ones shown in

picture 2.22.

Figure 2.22 Limit values of horizontal force H for intermediate pile prevented to rotate in cohesionless soil,

2.4.2.2 3D Strain Wedge model

Ashour and Norris (2001) developed the strain wedge model that allows the assessment of

the non-linear p-y curve of a laterally loaded pile without the use of non-linear springs.

The strain wedge model parameters are related to an envisioned 3D passive wedge of soil

developing in front of the pile (figure 2.23). The basic purpose is to relate stress-strain-

strength behavior of the soil in the wedge to one dimensional BEF parameters. The model



STATE OF THE ART 25

is, therefore, able to provide a theoretical link between the more complex three-dimensional

soil-pile interaction and the simpler one-dimensional BEF characterization.

The properties of the model are the base angles (βm), the passive wedge depth (DW), and

spread of wedge angle (φm, the mobilized friction angle).

One of the main assumptions associated with the SW model is that the deflection pattern of

the pile is taken to be linear over the controlling depth of the soil near the pile top, resulting

in a linearized deflection angle δ as seen in figure 2.24.

Figure 2.23 Basic strain wedge in uniform soil

Figure 2.24 Deflection pattern of laterally loaded long pile and associated strain wedge



STATE OF THE ART 26

The model can be adopted also for layered soils

2.4.3 Lateral displacement

Usually elastic analytical idealizations are not sufficient and numerical methods are used in

order to solve the problem.

The response of a pile subjected to lateral loads is represented through the so called “P-y”

curves where P is the horizontal load and y is the lateral displacement. These curves have a

strongly non-linear behavior and they are obtained modeling the foundation as an elastic

beam embedded in a non-linear spring bed, as explained in figure 2.26.

They are represented by an initial stiffness (represented by the tangent line to the first part

of the curve) and by a limit load that is reached when the curve becomes horizontal (pile-

soil system collapse).

These curves can vary due to several factors: soil characteristics, loading mode, pile head

constraints and installation procedures.

Figure 2.25 Proposed geometry of compound passive wedge



STATE OF THE ART 27

2.4.3.1 Loading mode

The external force can be applied in 3 different ways:

• Monotonic load: the target value of the force is reached through several small load

increments in order to avoid the arise of inertia forces. Each load increment is applied

when the effect of the previous one is finished. The waiting time to apply a load

increment depends on the soil type. Usually it is few seconds for granular soil, while

for clays is higher.

• Dynamic load: the target load is reached very fast and so inertia forces arise. It is

often used to simulate earthquake effects.

• Cyclic load: characterized by the alternating between loading and unloading phases.

2.4.3.2 Pile head constraint

Two extreme cases are discussed: pile head free to rotate and pile head prevented from

rotating. For the same load level, displacements of pile head are larger in the “free” case

because in the constrained case the pile-soil interactions are deeper. These constraints

conditions also influence the distribution of stresses along the pile. The different deformed

shapes for these two types of boundary conditions are depicted in figure 2.27 while bending

moments are shown in figure 2.28.

Figure 2.26 Principle for describing soil behavior with p-y curves (API, 2000)



STATE OF THE ART 28

2.4.3.3 Installation procedure

The installation technique influences the response of piles in both axial and lateral

solicitations because it changes the tensional state of soil at pile-soil interface. Horizontal

stresses increase with respect to the geostatic ones in driven piles because of the soil

movement due to installation blows. Conversely, horizontal tensions decrease in bored piles

because of the removal of soil during the installation.

Some authors like O’ Neill & Dunnavant (1984) and Alizadeh & Davisson (1970) studied

the problem with full-scale experiments. They found out that the installation procedure has

an influence on the pile behavior, but it is less important with respect to soil heterogeneity.

Moreover, the installation procedure effect is relevant just for small loading values.

Figure 2.28 Deformed shape diagrams for a pile free and prevented to rotate

Figure 2.27 Bending moment diagram for a pile free and prevented to rotate



STATE OF THE ART 29

2.5 Horizontal cyclic loads

Principal guide lines (API e DNV) don not focus so much in cyclic loaded monopiles

foundations. These standards use the ‘’p-y’’ curves based on few full-scale tests for long

piles (L/D=30) executed by Reese et al, 1974 and then they use a reduction factor, usually

0.9, in order to decrease the ultimate lateral resistance due to cyclic loads.

A more detailed degradation index was presented by Idriss et al. (1978) to describe the

change in stiffness and shape of the hysteresis loop as a function of the number of cycles.

𝛿 =

𝐸𝑠𝑁

𝐸𝑠1= 𝑁−𝑎 (2.16)

where EsN and Es1 are the secant moduli of the Nth and 1st cycle and a is the gradient of the

regression line in logarithmic scale (figure 2.29).

Long and Vanneste (1994) performed 34 full-scale lateral load tests to investigate which

parameters influenced the behavior of the cyclically loaded pile. Tests varied in many

aspects from each other: type of pile and construction method, length and diameter of the

pile, number of cycles, and load characteristics. The slenderness ratio varied from 3 to 84

(from very rigid to flexible piles) and the granular soils spanned from loose to dense

compaction. The piles were loaded in different ways: from 5 to 500 load cycles both in

symmetric and asymmetric loading conditions. They determined a degradation factor, m:

𝑚 = 0.17 ∙ 𝐹𝑙 ∙ 𝐹𝑖 ∙ 𝐹𝑑 (2.17)

Figure 2.29 Degradation of stiffness after number of cycles



STATE OF THE ART 30

Where F are factors that account for cyclic load ratio, installation method and soil density,

respectively. The cyclic load ratio is defined as the ratio between the minimum and

maximum amplitudes of the lateral load.

Static nonlinear P-y curves can be then obtained from the expressions given by the authors

for calculating soil resistance p and the displacement y

𝑃𝑁 = 𝑃1𝑁(𝛼−1)𝑚 (2.18)

𝑦𝑁 = 𝑦1𝑁𝛼𝑚 (2.19)

where N denotes the Nth cycle and 1 denotes the 1st cycle. The factor α controls the relative

contribution of soil resistance and deflection, and was applied to change the p –y relation

with depth. α varies from 0 to 1, but since its variation did not provide any improvement in

results, a constant value of α = 0.6 was applied, making the method independent of depth.

At the end of the study, it was found that the degradation of p-y curves was greater for 1-

way cyclic loading, for looser sand and for backfilled and drilled pile.

Lin and Liao (1999) also developed an expression in order to find a degradation parameter

t. Accounting for different model properties, the purpose of the study was the calculation of

the accumulation of pile displacements during load cycles. They performed 26 full-scale

lateral load tests. Pile slenderness ratios varied from 4 to 84 and the maximum number of

load cycles was 100. They derived the same factor of influence by Long and Vanneste (1994)

with the addition of a degradation factor dependent on pile-soil relative stiffness ratio

expressed by a depth coefficient, L/T.

𝑡 =

𝐿

𝑇𝜂𝛽𝜉𝜑 (2.20)

where the coefficient η changes with the model parameters such as soil density, load

characteristic and method of installation. 𝜑 is the cyclic load ratio, 𝜉 accounts for the

installation method and 𝛽 for the soil density. The relationship between strain and

displacement proposed by Kagawa and Kraft (1980) was used to determine the accumulated

displacement:

휀 =𝑦

2.5𝐷 (2.21)



STATE OF THE ART 31

where D is the diameter of the pile.

Strains as a function of load cycles where then determined using the strain ratio Rs expressed

by a logarithmic function:

𝑅𝑠 =휀𝑁

휀1= 1 + 𝑡 ln(𝑁) (2.22)

Where 휀𝑁 is the strain accumulation after N cycles and 휀1 is the strain after the first cycle.

Furthermore, Achmus et al. (2009) studied the degradation of stiffness in cohesionless soils

because of cyclic loading. Using triaxial tests and finite element method, they developed

design charts for determining deflection along piles as function of the number of cycles

The degradation is expressed by means of the ratio of the secant elastic modulus 𝐸𝑠 which

is elastic and dependent on the stress conditions along the pile.

𝐸𝑠 = 𝑘𝜎𝑎𝑡 (

𝜎𝑚

𝜎𝑎𝑡)

𝜆

(2.23)

where k and λ are material parameters and 𝜎𝑎𝑡 and 𝜎𝑚 are atmospheric pressure and mean

principal stress, respectively.

The accumulation of strains and thereby the plastic strain ratio is estimated by a semi-

empirical approach presented by Huurman (1996):

𝐸𝑠𝑁

𝐸𝑠1≅

휀𝑐𝑝1

휀𝑐𝑝𝑁

= 𝑁−𝑏1(𝑋)𝑏2 (2.24)

where εcp is the plastic axial strain, b1 and b2 are material parameters and X is the cyclic

stress ratio which defines the relation between maximum principal stresses for cyclic stress

state and static failure state.

Since during cyclic loading in triaxial tests the initial stress state is isotropic with constant

confining pressure while in real conditions stresses are anisotropic, a characteristic cyclic

stress ratio, Xc, is introduced:



STATE OF THE ART 32

𝑋𝑐 =

𝑋𝐿 − 𝑋𝑈

1 − 𝑋𝑈 (2.25)

where L and U define loading and unloading states.

The outcomes of the study are design charts for preliminary design providing the deflection

as function of number of load cycles up to 10000 cycles. However, the study lacks the

support of full- or small-scale tests.

For monotonic load, the chart in figure 2.30 was developed.

Concerning cyclic lateral load, it was found, as expected, a very big dependence on the ratio

between embedded length and pile diameter. Thus, in order to improve monopile

performance, the increase of pile length is much more effective than increasing the pile

diameter as observed in figure 2.31 and 2.32.

Figure 2.30 Lateral displacement of monopiles under static lateral load with regard to normalized load



STATE OF THE ART 33

Results for monopiles with diameters of 7.5 m and 2.5 m are compared in figure 2.33. The

smaller monopile exhibits much larger deformation than the larger monopile and thus has a

worse cyclic load performance. However, this pile has negligible rotation of its toe. Whereas

the large diameter pile shows very good cyclic performance, but the toe rotation is much

higher.

Figure 2.32 Effect of embedded length on the accumulation rate after 100 cycles for a monopile with D=5m, Tp=0.09m,

H=5MN and h=20m

Figure 2.33 Effect of pile diameter on the accumulated rate after 100 cycles for a monopile with L=20m, Tp=0.09m,

H=10MN and h=4m

Figure 2.31Comparison of clamping effect for piles with different diameters:(a) D=7.5m (b) D=2.5m



STATE OF THE ART 34

LeBlanc et al. (2010a) made 21 monotonic and cyclic tests on piles in sand with relative

densities of 0.04 and 0.38; the pile had a diameter of 80 mm and a slenderness ratio of 4.5.

The load characteristics are defined by the ratios ζb and ζc.

𝜉𝑏 =

𝑀𝑚𝑎𝑥

𝑀𝑠 (2.26)

𝜉𝑐 =

𝑀𝑚𝑖𝑛

𝑀𝑚𝑎𝑥 (2.27)

Where 𝑀𝑚𝑎𝑥 is the maximum cyclic moment, 𝑀𝑠 is the maximum static moment capacity

and 𝑀𝑚𝑖𝑛 is the minimum moment.

Tests were conducted with variation in 𝜉𝑏 from 0.2 to 0.53 and 𝜉𝑐 from -1 to 1 applying static

loads and one-way and two-way cyclic loads. The number of load cycles also varied from

approximately 8000 to 65000. According to LeBlanc et al. the best fit of the accumulation

of rotation is a power function:

Δ𝜃(𝑁)

𝜃𝑠=

𝜃𝑁 − 𝜃1

𝜃𝑠= 𝑇𝑏(𝜉𝑏, 𝑅𝑑)𝑇𝑐(𝜉𝑐)𝑁0.31 (2.28)

where, as shown in figure 2.34, 𝜃𝑁 is the rotation at N cycles, 𝜃1 is the rotation after the first

load cycle and 𝜃𝑠 is the rotation in a static test at a load equivalent to the one provided by

the maximum cyclic load. 𝑇𝑏 and 𝑇𝑐 are dimensionless functions depending on the load

characteristics and relative density. 𝑇𝑏 linearly depends on 𝜉𝑏 and Dr while a non-linear

dependency is found between 𝑇𝑐 and ζc. The largest accumulated rotation happens when 𝜉𝑐=

-0.6 which is a two-way loading.

Figure 2.34 Method for determination of stiffness and accumulated rotation: (a) cyclic test; (b) static test



STATE OF THE ART 35

Achmus et al. (2011) presented a finite element model based on strain degradation to verify

the results obtained by LeBlanc et al. (2010a) and they found good agreement between the

simulations and test results as reported in figure 2.35.

On the contrary, the study of the change of stiffness of soil-pile system did not provide as

clear results as the rotation accumulation. It is not possible to conclude how the stiffness is

affected by the relative density. However, every test shows an increase in stiffness with the

increase of load cycles number. This increase is contradictory to current methodology which

uses degradation of static p -y curves to account for cyclic loading.

Finally, Houlsby, Byrne et al, 2017 tried to investigate and develop improved design

methods for laterally loaded monopiles in the so-called PISA project.

The adopted approach was to validate 3D numerical models using medium scale field tests

and to investigate the performance of the existing p-y design method. These models were

then used to form the basis for developing an improved method capable of accurately

capturing the behavior of horizontally loaded monopiles.

Figure 2.35 Measured displacements as a function of N, Rd, 𝜉𝑏 and 𝜉𝑐. Dotted lines are obtained by using equation 2.28



STATE OF THE ART 36

The numerical model has been developed using the FE software ICFEP, employing high-

order displacement based isoparametric finite elements. The behaviour of dense sand was

reproduced with a bounding surface plasticity type model while the pile-soil interface was

simulated with an elastoplastic constitutive model whit zero strength if loaded in tension and

with compressive strength of the surrounding soil if loaded in compression. The former

characteristic enables the opening of a gap around the pile during lateral loading.

The medium-scale model was developed both for clay and sand with pile diameters of

0.273m, 0.762m and 2.0m and embedded lengths between 1.43m and 10.5m, providing a

range of normalized length 3 ≤ L/D ≤ 10 (figure 2.36). Figure 2.37 shows the loading

increment procedure: tests were predominantly carried under displacement controlled

monotonic conditions, supplemented with 1-way and 2-way cyclic loading.

Figure 2.37 Images of the small (D=0.273m), medium (D=0.726m) and large (D=2m) diameter test arrangements

Figure 2.36 Field pile load test procedure



STATE OF THE ART 37

The load-displacement response clearly shows that creep occurs when the load is maintained

at different load increments. On unloading and reloading there is a marginally stiffer

response and on further loading there is more plasticity once the previous loads have been

exceeded. Unloading at the end of the test saw significant recovery of displacement,

particularly for the longer pile. As expected, there is a defined relationship between

embedment depth and both stiffness and capacity. The shorter pile shows more evidence of

reaching a defined bearing capacity whereas the longer pile continues to pick up capacity

with displacement even at the defined failure displacement.

The ground level load-displacement comparison between a field test result, the numerical

prediction using the developed 3D FE and the traditional p-y approach is provided in figure

2.38.

It is clear that the traditional p-y approach neither captures the initial stiffness nor the

capacity of the pile, underestimating both by significant factors.

Figure 2.38 Comparison of ground level load-displacement response for L/D=5.25 and D=0.726m



STATE OF THE ART 38

2.6 Inclined loads

Few studies were made in order to find the response of piles subjected to inclined loads and

contrasting results were obtained.

Zeng li et al (2015) investigated the 3D failure envelope of a single flexible pile in sand

through a numerical model. Soil was modeled with a hypoplastic constitutive law while the

pile was modeled as an elastic beam with a length of 13 m, a diameter of 0.72 and a

slenderness ratio of 18.

To investigate the form of the failure surface in the H-V plane, free pile head conditions

(M=0) were considered. A displacement was applied on the top of the pile head (that could

rotate freely) in a certain direction. The angle of the displacement varied from 0° to 360° to

scan the failure surface in all the possible directions as depicted in figure 2.39.

The final strength was chosen as the point where numerical calculation diverged. By

connecting the values at the ends of the different load paths the complete failure surface was

thus obtained. Examples of load paths in the H-V plane from the numerical radial

displacement tests are shown in figure 2.40 (a). Numerical swipe tests were also performed

in H-V plane, figure 2.40(b) and for more complex loads in figure 2.40(c). A large number

(around 500) of numerical radial displacement tests were performed and the ultimate

strength (or failure locus) of each test is plotted in figure 2.40 (d).

Figure 2.39 Radial displacements tests in the H-V plane



STATE OF THE ART 39

Results were then compared with the semi-empirical formula of Meyerhof and Ranjan

(1972) to evaluate the interaction between the horizontal and vertical forces:

(

𝐻

𝐻0)

2

+ (𝑉

𝑉0)

2

= 1 (2.29)

where H0 and V0 are the horizontal and vertical bearing capacities of the pile. Equation 2.29

can be written in a normalized form as follows:

𝑓 = 𝑚2 + 𝑣2 − 1 (2.30)

Where m=H/H0 and v=V/Vc0 in compression or v=V=Vt0 in tension. m and v are dimensionless

quantities. The comparison of the semi-empirical equation 2.30 with the numerical results is

shown in figure 2.41 (a) and (b). The agreement is satisfactory although some discrepancies

are identified in the tension part (dash line).

Figure 2.40 Selected load paths from numerical radial displacement test (a), load paths from numerical swipe test (b),

numerical swipe tests with more complex load paths (c) and complete results from numerical radial displacement test (d),

in H-V plane (M=0)



STATE OF THE ART 40

Pusadkar and Ghormode (2015) also performed numerical simulations to study the problem.

They analized the behaviour of a pile in a two layered soil mass using MIDAS 3D. The soil

was modeled through Mohr-Coulomb constitutive soil model and the pile was taken as a

linear elastic beam structure made of concrete. The analysis was conducted on weak over

strong soil where the upper soil layer was taken as half the length of the length of the pile as

shown in figure 2.42.

Figure 2.41 Comparison of equation 2.29 with the numerical results (a) in the H-V plane and (b) in the normalized space

Figure 2.42 Problem model



STATE OF THE ART 41

Both inclination of the pile and inclination of the applied load where investigated. For a

vertical pile, they found that the maximum uplift capacity corresponds to an inclination of

the load of 20°. Then, the uplift capacity reduces if load inclination is more than 20°. The

obtained results are shown in figure 2.43.

Figure 2.43 Uplift capacity versus length of the pile (L) for D=0.3m



LABORATORY MODEL 42

3 LABORATORY MODEL

The first part of the chapter describes the experimental apparatus, the test installation

procedure and the testing program. In the second part, experimental results are compared

and commented

3.1 Experimental apparatus

All the experimental parts were settled on a rigid external structure composed of 12 metal

beams H140 in order to guarantee enough stiffness. The structure was originally designed

for small-scale tests on shallow foundation and it was later converted in order to

accommodate the devices used in this study.

The main body of the testing apparatus is composed by 5 elements (figure 3.1):

• The tank

• The distribution caisson

• The box

• The loading apparatus

• The measuring apparatus

Figure 3.1 Main body of the apparatus



LABORATORY MODEL 43

3.1.1 The tank

The tank is a wooden container were the sand is located before the deposition. It has a depth

of 470 mm and a thickness of 300 mm and it is 1250 mm long (figure 3.2). The bottom of

the tank consists in 2 plastic grids with circular holes: one is fixed while the other can shift

so that holes can be opened and closed (figure 3.3).

The caisson is located above all the other facilities and fixed to a cart that moves on rails,

fixed on the top horizontal beams of the external structure. Those rails allow an easy

movement of the tank during the refilling and the positioning operations. Furthermore, the

container can also raise and lower. Once the tank is placed right above the box, grids are

opened and sand falls in the underneath box.

By combining the spacing and the radius of the grid holes and the falling height, it is possible

to obtain a sand deposit with a desired relative density. This procedure is called “pluviation.

Figure 3.2 Tank lateral view

Figure 3.3 Grids



LABORATORY MODEL 44

3.1.2 The distribution caisson

The distribution caisson is a plexiglass hollow rectangle placed between the tank and the box

during the deposition operations (figure 3.4). Its main function is to guarantee a more

uniform and homogeneous deposition and to avoid the dispersion of sand outside the box.

3.1.3 The box

The box is the container where the tests take place. It has a depth of 400 mm and a thickness

of 200mm and it is 870 mm long (figure 3.5).

It is entirely made by wood except for the frontal walls made in 10 mm thick tempered glass.

The two larger walls are reinforced with 3 tie rods with a diameter of 8 mm in order to

increase wall stiffness and to avoid out-of-plane movements

Figure 3.4 The distribution caisson

Figure 3.5 The box



LABORATORY MODEL 45

3.1.4 Loading apparatus

The loading apparatus consists in two cylindrical Bellofram pistons shown in figure 3.6 (a)

and (b). They are placed in perpendicular directions, so that it is possible to apply two

independent forces in both the horizontal and vertical direction.

The pistons are fixed to a metal cart that moves on rails fixed on the mid-height horizontal

beam of the external structure. This allow to easily translate the loading apparatus in order

to not influence the deposition process.

Pistons are connected to the pression control panel of the control station, which allows the

independent regulation of each of the two pression chambers inside the pistons.

In one chamber, pression is regulated by a 4-20 mA valve while in the other one it is

regulated by a manual regulator. This allow applying at the beginning of the test a pressure

from 20 to 700 KPa and to keep it constant during the whole test.

The control signal varies from 0 to 10 Volt and it is regulated by a D/A 12bit converter with

a precision of ±5kPa

Figure 3.6 Loading apparatus: (a), the horizontal piston, (b) the cart with the vertical piston

(a) (b)



LABORATORY MODEL 46

3.1.5 Measurement apparatus

The measured quantities are the applied load - through load cells- and pile displacements -

through displacement transducers.

3.1.5.1 Load cells

Two load cells are used, to measure the vertical and the horizontal forces, respectively. They

are placed between the pistons and the metal parts to whom the pile is constrained.

The horizontal load cell (figure 3.7a) has a maximum capacity of 960 N, with an estimated

precision of ±1.5N. The vertical cell (figure 3.7b) has a maximum capacity of 1960 N and

an estimated precision of ±0.5N.

3.1.5.2 Displacements transducers

Two Luchsinger LDT-AMP displacement transducers were used, for the vertical and the

horizontal displacements.

They can measure displacements up to 50 mm with a precision of ± 0.05 mm and they are

both fixed to steel bars in turn fixed to the external structure.

(a) (b)

Figure 3.7 Load cells: (a) horizontal, (b) vertical

(a) (b)



LABORATORY MODEL 47

The vertical transducer measures the displacements of a flat steel bar fixed to the pile head

(figure 3.8 a). The horizontal transducer measures the displacement of a PVC bar screwed

to the metal constraint of the pile which moves with it (figure 3.8 b).

3.1.6 Control station

The control station is in front of the main body and it is composed by a computer and a

pressure control panel.

3.1.6.1 Software

Tests are controlled by a dedicated software developed by Laboratorio Prove Materiali in a

LabVIEW environment, managing the post-processed data through an A/D 16-bit converter

(Figure 3.9).

The software allows to regulate pressure on the piston, to upload loading pattern files and to

visualize in real time the time trends of vertical and horizontal displacements, forces and

pressures. Loading patterns are uploaded in a .dat format. It was also developed a special

power device station for all the electronic measuring tools in order to guarantee a better

reliability of measurements (figure 3.10)

(a) (b)

Figure 3.8 (a) Vertical and (b) horizontal transducers



LABORATORY MODEL 48

3.1.6.2 Pressure control panel

Pressure is electronically controlled by electronic pressure transducers with a capacity of

1000 kPa and a precision of ±2kPa (figure 3.11).

Figure 3.10 Power station for measuring instruments

Figure 3.9 Software display



LABORATORY MODEL 49

The same pression system can be also manually controlled by knobs so that pressure can be

easily regulated.Two pressure lines are adopted: one connected to the vertical piston and one

connected to the horizontal piston.

3.1.7 Calibration

Calibration consists in determining the link between the microvolts measured by electronic

instruments to the physical quantity the tool is intended to measure.

Once the calibration law is known, it is implemented in the software, so that is possible to

visualize directly the proper unit of measurement instead of microvolts. Instruments were

calibrated more times during the testing period.

3 types of measuring instruments are adopted:

• Displacements transducers, in order to measure pile displacements both in horizontal

and vertical direction.

• Pressure transducers, in order to measure the piston pressure on the pile both in

horizontal and vertical direction.

• Load cells, in order to measure the applied load on the pile both in horizontal and

vertical direction.

Figure 3.11 Pressure control panel



LABORATORY MODEL 50

3.1.7.1 Displacements transducers calibration

In order to calibrate the displacement transducers a micrometer (figure 3.12) has been used.

The calibration procedure consists in manually imposing a known displacement to the

transducers and measuring the corresponding microvolt variation. A linear relationship

between displacements and voltage has been obtained (figure 3.13 and 3.14)

Figure 3.12 Micrometer

0

10

20

30

40

50

60

0 1000000 2000000 3000000 4000000 5000000

Dis

pla

cem

ents

[m

m]

Voltage [mV]

Horizontal transducer calibration

Figure 3.13 Horizontal transducer calibration



LABORATORY MODEL 51

3.1.7.2 Load cells calibration

In this case, link between voltage and force is obtained.

The load cell is hanged up on a metal support structure and metal plates are gradually hooked

to the cell preventing any rotation (figure 3.15).

0

10

20

30

40

50

60

0 1000000 2000000 3000000 4000000 5000000

Dis

pla

cem

ents

[m

m]

Voltage [mV]

Vertical transducer calibration

Figure 3.14 Vertical transducer calibration

Figure 3.15 Metal structure adopted to calibrate load cells



LABORATORY MODEL 52

The first measurement corresponds to the unloaded cell; then, metal plates of 10 or 20 Kg

are added in step in order to simulate a load increment and the relevant voltage variation is

read. The process has been performed for both the vertical and the horizontal cell. The

obtained linear relationships are shown in figures 3.16 and 3.17.

0

200

400

600

800

1000

1200

1400

1600

1800

0 1000000 2000000 3000000 4000000 5000000 6000000 7000000 8000000 9000000

Fo

rce

[N]

Voltage [mV]

Vertical cell calibration

Figure 3.16 Vertical cell calibration

0

100

200

300

400

500

600

700

800

900

0 1000000 2000000 3000000 4000000 5000000 6000000 7000000 8000000 9000000

Fo

rce

[N

]

Voltage [mV]

Horizontal cell calibration

Figure 3.17 Horizontal cell calibration



LABORATORY MODEL 53

3.1.7.3 Pressure cells calibration

The process of calibration of pressure cells consists in increasing step-by-step the hydraulic

pressure acting on the cells through a manual pump up to their maximum capacity equal to

1000 kPa. The two cells (horizontal and vertical) are connected to the pump through low-

deformable plastic pipes so it is possible to execute the procedure once. The obtained linear

relationships are shown in the figures 3.18 and 3.19.

0

100

200

300

400

500

600

700

0 2 4 6 8 10 12

Pre

ssio

n [

kP

a]

Voltage [V]

Horizontal pressure cell calibration

Figure 3.18 Horizontal pressure cell calibration

0

100

200

300

400

500

600

700

0 2 4 6 8 10 12

Pre

ssu

re [

kP

a]

Voltage [V]

Vertical pressure cell calibration

Figure 3.19 Vertical pressure cell calibration



LABORATORY MODEL 54

3.1.8 The foundation system

The foundation system is composed by the pile and the sleeve.

3.1.8.1 The pile

All the tests were carried out with the same circular full-section monopile. The slenderness

ratio of the pile is L/D ≈ 4.17 (figure 3.20). On the head of the pile it was realized a M10

thread in order to accommodate a smaller steel pile that works as an extension of the pile

and where it is possible to insert the sleeve. All the pile features are listed on table 3.1.

Table 3.1 Pile features

Pile features

Material

Inox steel AISI 304

Weight W (𝑁) 63.743

Density D (𝐾𝑔

𝑑𝑚3) 7.9

Poisson’s

coefficient ν (/) 0.3

Elastic modulus E (𝑁

𝑚𝑚2) 200000

Lenght L ( 𝑚𝑚) 250

Diameter D ( 𝑚𝑚) 60

Figure 3.20 Pile model



LABORATORY MODEL 55

3.1.8.2 The sleeve

The sleeve is a rectangular metal box with a circular cavity (figure 3.21). Cavity walls

accommodate recirculating balls screws in order to facilitate the small pile penetration.

The sleeve can be screwed to the metal part where the horizontal piston acts so that it allows

the transmission of the horizontal force to the pile.

This constraint allows just rigid body translation and prevent any rotation.

3.1.9 Soil used in the investigation

3.1.9.1 Sand properties

The soil used in the investigation is the well-known Ticino sand. Its granulometric properties

and mechanical parameters have been obtained by Fioravante (2000), as shown in table 3.2.

The granulometric curve of the material is shown in figure 3.22.

Figure 3.21 The sleeve

Figure 3.22 Granulometric curve of Ticino sand



LABORATORY MODEL 56

Table 3.2 sand features

Sand features

Material Ticino river’s sand

Solid unit weight Gs (-) 2.67

Average grain size D50 (𝑚𝑚) 0.55

Uniformity coefficient Uc (-) 1.6

Minimum specific weight γmin (𝑘𝑁

𝑚3) 13.65

Maximum specific weight γmax (𝑘𝑁

𝑚3) 16.67

Minimum void ratio emin (-) 0.578

Maximum void ratio emax (-) 0.927

Critical friction angle Φ’cv (°) 34.6

Changing the grids of the tank it is possible to obtain different values of relative density. As

suggested by Calogni and Savoldi (2000), the use of a grid with 20 mm diameter holes and

a spacing of 60 mm leads to a relative density of 40%, while the use of a grid with 4 mm

holes and 25 mm spacing of leads to a relative density of 90%.

In order to simulate a dense sand, it was used a grid with holes of 4 mm and a spacing of 25

mm, while to simulate a loose sand it was used a grid with holes of 15 mm and a spacing of

40 mm. The respective values of relative density were then validated.



LABORATORY MODEL 57

3.1.9.2 Relative density evaluation

Relative density of cohesionless soils is defined as

𝐷𝑟 =𝑒𝑚𝑎𝑥 − 𝑒

𝑒𝑚𝑎𝑥 − 𝑒𝑚𝑖𝑛 (3.1)

where emax is the maximum void ratio of soil corresponding to the loosest state, e is the

current void ratio, and emin is the minimum void ratio of soil corresponding to the densest

state.

To determine the relative density, it is necessary to determine the specific gravity of soils in

order to calculate the void ratio from dry density in the loosest, current, and densest states.

It is useful to express relative density directly in terms of dry density in loosest, in-situ, and

densest states, so that the need to determine the specific gravity of soil is eliminated. The

current void ratio of soil is given by the relation

𝑒 =

𝐺𝛾𝑤

𝛾𝑑− 1 (3.2)

Where, γw = unit weight of water (9.81 kN/m3)

Similarly, the maximum and minimum void ratio of soil corresponding to loosest and densest

states are given, respectively, by

𝑒𝑚𝑎𝑥 =𝐺𝛾𝑤

𝛾𝑑 𝑚𝑎𝑥− 1

(3.3)

𝑒𝑚𝑖𝑛 =𝐺𝛾𝑤

𝛾𝑑 𝑚𝑖𝑛− 1

(3.4)

Substituting these values in Eq. (3.1), it is obtained the expression for relative density as

𝐷𝑟 =[(

𝐺𝛾𝑤

𝛾𝑑 𝑚𝑖𝑛)−(

𝐺𝛾𝑤

𝛾𝑑 )]

[(𝐺𝛾𝑤


𝐺𝛾𝑤

𝛾𝑑 𝑚𝑎𝑥)]

(3.5)



LABORATORY MODEL 58

𝐷𝑟 =[(

1𝛾𝑑 𝑚𝑖𝑛

)−(1

𝛾𝑑 )]

[(1


1𝛾𝑑 𝑚𝑎𝑥

)]

(3.6)

𝐷𝑟 =

[(𝛾𝑑 −𝛾𝑑 𝑚𝑖𝑛

𝛾𝑑 𝑚𝑖𝑛𝛾𝑑 )]

[(𝛾𝑑 𝑚𝑎𝑥 −𝛾𝑑 𝑚𝑖𝑛

𝛾𝑑 𝑚𝑖𝑛𝛾𝑑 𝑚𝑎𝑥)]

(3.7)

𝐷𝑟 =𝛾𝑑 𝑚𝑎𝑥

𝛾𝑑[

𝛾𝑑 − 𝛾𝑑𝑚𝑖𝑛

𝛾𝑑𝑚𝑎𝑥 − 𝛾𝑑𝑚𝑖𝑛] (3.8)

Thus, the relative density computation is reduced to the determination of the dry specific

weight 𝛾𝑑 .

In order to measure 𝛾𝑑 , a pycnometer is placed at the bottom of the sand box (Figure 3.23)

and then the deposition process is carried out. At the end, the pycnometer full of sand is

removed and weighed. Knowing the weight of sand Ws and the pycnometer volume V, it is

possible to calculate 𝛾𝑑 as:

The obtained quantities for the two type of grid are reported in table 3.3: the values of relative

density are approximately 50% for loose sand and 85% for dense sand.

𝛾𝑑 =

𝑊𝑠

𝑉

(3.9)

Figure 3.23 The pycnometer placed inside the box



LABORATORY MODEL 59

Table 3.3Relative density computation

3.1.9.3 Size effect

A useful parameter for considering size effect is the ratio

𝐷

𝑑50

(3.10)

Where D is the pile diameter. In the present case:

𝐷 = 60 𝑚𝑚

𝑑50 = 0.55 𝑚𝑚

Where 𝑑50 was found from the granulometric curve of figure 3.22.

According to Remaud (1999), size effects are negligible if the ratio (3.10) is larger than 60,

while for Garnier and Konig (1998), size effects are negligible if the ratio is larger than 100.

In this case, the ratio is 110 so both verifications are fulfilled: sand can thus be considered

as a continuum for calculation purposed.

Relative density computation

Sand weight (kN) 0.0863 0.0925

Volume (m3) 0.0057 0.0058

γD (kN/m3) 14.9933 16.0671

e (-) 0.7470 0.6302

Dr (%) 51.5% ≈ 50% 85.05 % ≈ 85%



LABORATORY MODEL 60

3.2 Installation process

The installation procedure for driven piles can be summarized in the following steps:

1. The box full of sand from the previous test is emptied for ¾ of its height and sand is

put in the upper tank.

2. The distribution caisson is fixed between the upper tank and the lower box. A plastic

net is placed over the box to guarantee a better sand distribution and avoid

disturbance during the removal of sand surplus.

3. Grids are opened and sand starts to rain in the box below.

4. Sand excess is removed, and the plastic net is taken away.

5. A system of metal guides is fixed to the external structure and to the sand box in

order to sustain a plexiglass pipe with a height of 1 m and an internal diameter of 65

mm (figure 3.24).

6. The pile is placed over the sand and its verticality controlled through a bubble level.

7. The plexiglass pipe is slipped around the pile and fixed.

8. A steel plate is put on pilehead to protect it from hits.

Figure 3.24 Installed metal guides



LABORATORY MODEL 61

9. An iron mallet of 1 kg is raised and dropped inside the pipe so it can hit the pile

vertically (figure 3.25).

10. The hitting procedure is stopped after some intervals and the pipe is removed in order

to check the verticality with the bubble level and the sinking with a set square.

11. Once the pile has sunk of 1 cm under the sand level, all the beating instruments are

removed and the cart carrying the pistons placed over pile head.

12. A smaller pile is screwed to the head of the pile. The flat steel bar for vertical

displacement measurements is placed between the two piles (Figure 3.26).

Figure 3.25 The iron mallet inside the tube

Figure 3.26 Flat steel bar and smaller pile installed in the head of the embedded pile



LABORATORY MODEL 62

13. The sleeve is inserted on the small pile and then it is screwed to the metal part to

whom the horizontal piston and the horizontal load cell acts.

14. The vertical load cell is connected directly to the small pile head with a screw and

the displacement transducers are put in place (figure 3.27).

15. Load patterns are applied thanks to the software.

The pile should penetrate in a perfectly vertical way because, as already reported in

paragraph 2.3.2.1, the pull-out resistance increases with inclinations lower than 20°. At the

same time the pile cannot be touched from operators in order to do not modify the interface

properties and relative density of the sand.

It follows that points 9 and 10 are very delicate and time consuming, making the average

duration of the installation procedure of about 1 hour and a half.

Figure 3.27 Final display of the apparatus before the application of load patterns



LABORATORY MODEL 63

3.3 Testing program

Two different relative densities of sand were tested. The relative density equal to 85% will

be referred as “dense sand” while the one with relative density equal to 50% will be referred

as “loose sand”.

Three different kind of test were performed: simple pullout, pullout after lateral cyclic load

and radial tests.

In simple pullout test, whose load pattern is shown in figure 3.28, just a vertical force in the

upward direction is applied on pile head after the installation of the pile, until the pullout

capacity of the pile is exceeded, and the pile starts to move in the upward direction.

Pullout tests after lateral cyclic load test, whose patterns are depicted in figure 3.29, are

divided into two phases. In the first phase, 1, 6 or 12 cycles of horizontal loading are applied;

then, in the second phase, a vertical upward load is applied until failure. Just asymmetric

horizontal cycles have been applied in order to mimic the relevant in situ conditions.

Different maximum horizontal loads of 30 N, 40 N, 50 N, 100 N, 200N and 300 N were

applied both for loose and dense sand.

Figure 3.29 Pull-out after lateral cyclic load patterns

Figure 3.28 Simple pull out load pattern



LABORATORY MODEL 64

In order to simplify test recognition, an alphanumerical code was assigned to every test.

The first number indicates the number of cycles, the second acronyms stands for the type

of load (HA stands for horizontal asymmetric load) and the last number denotes the

maximum lateral load reached in the test. So, for example, a pull-out test after 12 lateral

asymmetric cyclic loads at 300 N can be summarized as 12HA(300).

Additional specific tests at larger loads (1HA(500)) and at higher number of cycles

(100HA(200)) for dense and loose sand were performed to highlight some specific issues

of the behavior of the pile-sand system.

Finally, in radial test both vertical and horizontal forces are simultaneously applied up to

failure (figure 3.30). Radial tests have been performed just on loose sand for both driven and

pre-installed piles.For radial test, the imposed path can be described by the ratio between the

horizontal and vertical applied load 𝑉

𝐻. The employed load paths were 0 (simple pull-out),

0.25, 0.5, 0.625, 0.75, 0.875 and 1. Tests will be classified by the letter R followed by the

value of 𝑉

𝐻, for example R (0.25). In order to better draw the interacton domain, both tensile

and compression radial test were performed

Tests were conducted in load control conditions. For all the tests, the same fixed loading rate

have been imposed, equal to 0.42 𝑁/𝑠 (25 N every minute) for both vertical and horizontal

load. This rate is sufficiently slow to neglect dynamic effects.

The lists of all the performed test are summarized in table 3.4, table 3.5, table 3.6, table 3.7

and table 3.8.

Figure 3.30 Radial test load patterns



LABORATORY MODEL 65

Table 3.4 Performed pull out tests

Test Dense sand Loose sand

Simple pull out

Table 3.5 Performed pull out tests after lateral cyclic loading in loose sand

Driven pile in loose sand

Load [N] \ cycles 1 6 12 100

30

40

50

100

200

300

500



LABORATORY MODEL 66

Table 3.6 Performed pull out tests after lateral cyclic loading in dense sand

Table 3.7 Performed tensile radial tests in loose sand

Tensile redial test for driven pile in loose sand

H/V

0.25 ✔

0.5 ✔

0.625 ✔

0.75 ✔

0.875 ✔

1 ✔

Driven pile in dense sand

Load [N] \ cycles 1 6 12 100

30

40

50

100

200

300

500



LABORATORY MODEL 67

Table 3.8 Performed compression radial test for driven pile in loose sand

Compression radial test for driven pile in loose sand

H/V

0.25 ✔

0.375 ✔

0.5 ✔

In the following paragraphs, the outcome tests of simple pullout, pull out after lateral cyclic

loads and radial loads are commented. For the convenience of the reader, just some

representative results are listed. The complete list of experimental results and comparison

among them are contained in Appendix A.

3.4 Simple pullout test

Simple pullout tests were carried out for both dense and loose sand. Values of the vertical

tensile force are plotted as a function of vertical displacement in figure 3.31. The pullout

-40

-35

-30

-25

-20

-15

-10

-5

0

0 0,5 1 1,5 2 2,5 3

ver

tica

l fo

rce

[N]

vertical displacement [mm]

Simple pullout test

Loose sand

Dense sand

Figure 3.31Simple pullout test for the driven pile



LABORATORY MODEL 68

resistance is the peak applied force just before the pile starts to be extracted from the soil.

The measured value is then depurated from the self-weight of the pile 63. 743 N.

Experimental data clearly evidence that the tensile resistance in dense sand is higher with

respect to loose sand. The increase of pullout capacity with soil relative density can be

attributed to the fact that dilation occurs in dense sand when the pile tends to move upward.

This dilation increases the confinement forces that in turn increase shaft resistance. On the

contrary, when loose sand is subjected to shear stress, soil tends to compact, and no dilation

occurs.

These results can be compared to the ones obtained on pre-installed piles. Patera (2018)

performed the same tests with the same laboratory apparatus of the present work. The only

difference was the installation procedure: in the pre-installed case, the pile was cast in place

before sand deposition. In this way, sand densification around the pile due to impacts was

avoided.

Plots shown in figure 3.32 clearly evidence that the pullout capacity is larger for driven piles,

both for loose and dense sand. For the same installation process, piles installed in dense sand

have a larger pullout capacity. Furthermore, pullout resistance for loose sand in driven pile

is higher than pullout resistance for dense sand in pre-installed pile, evidencing the role of

the installation procedure on the process of pile extraction. During the driving procedure,

blows generate a denser sand ring around the pile, increasing the pullout capacity: a local

effect thus dominates the global response.



LABORATORY MODEL 69

In table 3.9 all the simple pullout forces values for both pre-installed and driven pile are

shown.

Table 3.9 Pullout forces for driven and pre-installed piles

Simple Pull-out

Pile type Sand type Measured force [N] Pull-out force [N]

(no pile self-weight)

Pre-installed Loose 77.45 13.70

Pre-installed Dense 82.41 18.67

Driven Loose 95.79 32.05

Driven Dense 101.82 38.08

Simple Pull-out

Pile type Sand type Measured force [N] Pullout force [N]






-40

-35

-30

-25

-20

-15

-10

-5

0

0 0,1 0,2 0,3 0,4

ver

tica

l fo

rce

[N]


Simple pullout

Driven pile in loose

sand

Driven pile in dense

sand

Pre-installed pile in

dense sand

Pre-installed piles in

loose sand

Figure 3.32 Simple pullout test for driven and pre-installed pile for loose and dense sand



LABORATORY MODEL 70

3.4.1 Estimation of interface friction angle

Interface friction angle was estimated for both loose and dense sand.

In order to evaluate the interface friction angle, the pullout capacity formula (equation 2.12)

proposed by Meyerhof (1973) was employed:

𝑃𝑢 = 𝜋𝐷𝛾𝐾𝑢 (

𝐿2

2) + 𝑊𝑃

(4.1)

Where D, L and Wp are the diameter, the length and the weight of the pile, 𝛾 the unit weight

of the soil and 𝐾𝑢 is the uplift coefficient:

𝐾𝑢 = 𝐾𝑃𝑡𝑎𝑛𝛿 (4.2)

Where 𝛿 is the interface friction angle and Kp is the passive thrust coefficient:

𝐾𝑃 =

1 + sin 𝜙 ′

1 − sin 𝜙′

(4.3)

Combining equations 4.1 and 4.2 it is possible to obtain the interface friction angle as:

𝛿 = tan−1 [

2(𝑃𝑢 − 𝑊𝑝)

𝜋𝐷𝛾𝐾𝑝𝐿2]

(4.5)

Knowing the value of 𝑃𝑢 from simple pull out laboratory tests, the obtained value for loose

sand is:

𝛿 ≅ 22°

While the obtained value for dense sand is

𝛿 ≅ 24°

It is worth noting that the Ticino river sand, according to Fioravante (2000) characterization,

has an internal friction angle of ϕ’=34.6°. A commonly used rough estimation of interface

friction angle is obtained through a relationship with the internal friction angle, in particular:



LABORATORY MODEL 71

𝛿 ≅

2

3∙ ϕ’ = 23°

Which is consistent with the obtained results of equation 4.5.

Some authors, like Viggiani (1999), suggest a more conservative value of 20° for the steel-

sand interface friction angle.



LABORATORY MODEL 72

3.5 Pull out after lateral cyclic load

This test will be argued in two separated sections: the first part (lateral load) will discuss the

lateral behavior of the pile-soil system while the second part (pullout) will focus on the

variation of the upliftt capacity as a function of the previous lateral cyclic load history.

3.5.1 Lateral behavior

3.5.1.1 Monotonic lateral behavior

For small value of horizontal force, for example 30 N, a typical curve for the driven pile can

be observed in figure 3.33.

Curves have a monotonic trend. The curve of loose sand shows a much larger displacement

of approximately 0.47 mm at the peak of loading phase. On the contrary, the curve of dense

sand shows a lateral displacement five times smaller with respect to the other curve and no

bending of the curve is observed.

By increasing the value of horizontal load, for example 200 N, a different result is obtained

as depicted in figure 3.34.

0

5

10

15

20

25

30

35

-0,5 -0,4 -0,3 -0,2 -0,1 0

hori

zonta

l fo

rce

[N]

horizontal displacement [mm]

1HA30 driven pile

dense sand

loose sand

Figure 3.33 Monotonic lateral load for 1HA30 test in loose and dense sand



LABORATORY MODEL 73

The dense sand curve still maintains a decreasing-stiffness trend, showing a much smaller

displacement than loose sand curve for the same force. The curve of loose sand not only

shows a larger displacement, but a change in concavity appears after a threshold

displacement. Two inflection can be noticed at a load level of approximately 30 N and 80

N. This kind of behavior was unexpected, and not predicted by any classical pile theory

To provide a physical interpretation of this response, under the assumption of a rigid-

perfectly plastic soil behavior, the displacement field that generates at failure in the soil

around a pile is analyzed. Increasing the depth, that will be indicated in a non-dimensional

way as z/D, the displacement vertical component of soil at failure tend to decrease, vanishing

for values z/D >4. (figure 3.35).

For high values of z/D, in fact, the displacement field lies just on the horizontal plane x-y

and can be studied as a plane strain problem. The failure domain is closed and the part of

soil that is being pushed on the left tends to flow back laterally and to go behind the pile

(figure 3.36b). The size of soil failure domain depends on pile diameter D and on soil

mechanical characteristics.

0

50

100

150

200

250

-12 -10 -8 -6 -4 -2 0

ho

rizo

nta

l fo

rce

[N]


1HA200 driven pile

dense sand

loose sand

Figure 3.34 Monotonic lateral load for 1HA200 test in loose and dense sand



LABORATORY MODEL 74

Vice versa, for small values of z/D, the so called “wall-effect” dominates at failure. The

failure domain is characterized by the presence of two approximately independent lobes, one

on the left and one on the right of the pile. Inside these two zones the displacement field is

characterized by two dominant components: one along z direction and the other along the x

direction. The state of stress is close to the one of active thrust on the left and passive thrust

on the right. Shear lateral stresses are negligible (figure 3.36).

Figure 3.35 Displacement field around a long pile

Figure 3.36 Failure mechanisms of a pile as a function of z/D



LABORATORY MODEL 75

For intermediate values of z/D, the reference failure mechanism is a mixture of the two

mechanisms. The more z/D increases, the more the tridimensional behavior of the problem

arises so that also lateral soil tends to progressively transfer part of the stresses on the

inclusion. Following the empirical approach of Brinch-Hansen (1961) for granular soil, the

lateral bearing capacity of the pile Ph is

𝑃ℎ = 𝛾 ∙ 𝑧 ∙ 𝐷 ∙ 𝑁𝑞(𝑧

𝐷, 𝜙′) (4.6)

Equation (4.6) is very similar to the trinomial formula of Terzaghi for shallow foundation

where just the term related to the depth of the footing and overburden pressure appears. The

terms associated to the weight for unit volume and cohesion are not present. In fact, cohesion

is equal to zero since the soil is granular and the power of soil weight is null since the

formation process mainly develops on the horizontal plane. According to Brinch-Hansen the

term 𝛾𝑧𝐷𝑁𝑞 can be found trough the evaluation of an equivalent cohesive force of the

granular soil at a certain depth z as 𝛾𝑧 tan 𝜙′. Consequentially, 𝑁𝑞 = 𝑁𝑐 tan 𝜙′ and its trend

can be observed in figure 3.37.

Figure 3.37 Variation of Nq with z/D and friction angle



LABORATORY MODEL 76

Formula (4.6) does not consider the contribution of the lateral overburden and this is because

on the reverse side of the pile soil stresses decrease because of the creation of an arch-effect

and so lateral overburden is extremely reduced.

In the case of a monopile foundation, the low value of the embedment ratio z/D does not

allow the deep mechanism to show and just the superficial one arises. The resulting system

can be assimilated to a sheet pile laterally loaded on its head. So, in other words, the problem

goes back to being bidimensional as depicted in figure 3.38. If the sheet pile is assumed to

be rigid, its failure mechanism is well known and, at every depth z, it is characterized by a

zone where the soil fails in passive thrust conditions and a zone where the soil fails in active

thrust conditions.

Before load application, the lateral pressure coefficient acting on the pile corresponds to the

at-rest one K0. Then, as soon as the load is applied, the pile starts to move, and the earth

thrust changes. In particular, it is possible to define two different earth pressure coefficients:

Kexp acting on the side of the pile where soil undergoes expansion, and Kcomp acting on the

side of the pile where soil undergoes compression. As the pile continues to move, Kexp

decreases from K0 to the active thrust coefficient at failure KA. On the contrary, Kcomp

increases from K0 to the passive thrust coefficient at failure KP.

The variation of lateral pressure coefficients with displacements is depicted in figure 3.39.

It is worth noting that Kexp and Kcomp have different incremental rates: while Kexp rapidly

decreases and after a small displacement reaches the failure value KA, Kcomp initially

increases at a slower rate, but reaches the failure value KP after much higher displacements.

Figure 3.38 Sheet pile failure mechanism



LABORATORY MODEL 77

So, both expansion and compression thrusts play a key role on the displacement of the pile,

and the force variation ΔP acting on the pile can be obtained as:

𝛥𝑃(𝛿) = 𝛾𝑧𝐷[𝛥𝐾(𝛿)] = 𝛾𝑧𝐷[𝛥𝐾𝑐𝑜𝑚𝑝(𝛿) − 𝛥𝐾𝑒𝑥𝑝(𝛿)] (4.9)

Where 𝛿 is the pile lateral displacement, 𝛾 the unit weight of the soil, D the pile diameter

and 𝛥𝐾𝑐𝑜𝑚𝑝(𝛿) and 𝛥𝐾𝑒𝑥𝑝(𝛿) the variation of lateral compression and expansion

coefficients.

Compression and extension thrusts act separately, behaving in practice as two independent

mechanisms. Consequentially, the unexpected double inflection shape observed in figure

3.34 can be explained thanks to the different variation of lateral pressure coefficients for the

same displacement.

Considering figure 3.40, three different part can be observed:

1. in the first part of the graph, as soon as the force is applied and displacements are

small, the active thrust coefficient rapidly decreases, 𝛥𝐾𝑒𝑥𝑝(𝛿) < 0, while the

passive thrust coefficient increases at a slower rate 𝛥𝐾𝑐𝑜𝑚𝑝(𝛿) > 0. The resultant

Δ𝐾(𝛿) > 0 and so an increase of the force P is observed: 𝛥𝑃(𝛿) > 0.

Figure 3.39 Lateral pressure coefficients trends

Kexp

Kcomp



LABORATORY MODEL 78

2. Increasing the displacements, 𝐾𝑐𝑜𝑚𝑝(𝛿) still slightly increases while 𝐾𝑒𝑥𝑝(𝛿)

slightly reduces. It follows that their difference remains more or less constant, Δ𝐾 ≈

0 and so the force does not increase: 𝛥𝑃(𝛿) ≈ 0.

3. Finally, when the displacements are considerable, the expansion coefficient remains

constant, 𝛥𝐾𝑒𝑥𝑝(𝛿) = 0 while the compression coefficient strongly increases,

𝛥𝐾𝑐𝑜𝑚𝑝(𝛿) > 0 and the curve rises again: 𝛥𝑃(𝛿) > 0.

Figure 3.40 , The three different phases during lateral loading.

The same behaviour can be observed in figure 3.41 for pre-installed piles. In loose sand, the

same trend of driven pile occurs but the first part of the curve (the first inflection) is reached

at a lower load level (20 N) and consequently the third part of the curve (after the second

inflection point) dominates the overall response. This is probably due to the absence of

densification caused by the driving processes that creates a sort of denser ring around the

pile where earth pressure coefficient is enhanced.

Pre-installed pile in dense sand shows an analogous behavior, but displacement is lower, and

the inclination of the curve is higher. This stiffer response is due to the lower void ratio with

respect to the loose sand case.

0

50

100

150

200

250

300

350

-14 -12 -10 -8 -6 -4 -2 0

hori

zon

tal fo

rce

[N]


1HA(300) driven pile in loose sand

2

3

1



LABORATORY MODEL 79

Figure 3.41 1HA400 test for pre-installed pile

Apparently, the only case that does not show the double inflection behavior is the driven pile

in dense sand. Probably, the already large density of the sand is enhanced by the installation

procedure, so that the applied horizontal forces are not large enough to reach the first

inflection point.

To investigate this aspect, a trial test at 500N was perfomed on the sand sand system, but, as

shown in figure 3.42, no inflection was again detected. To find the second inflection point it

is probably necessary to apply a larger horizontal load, that unfortunately cannot be provided

by the laboratory equipment in the present configuration.

0

50

100

150

200

250

300

350

400

450

-18 -16 -14 -12 -10 -8 -6 -4 -2 0

hori

zonta

l fo

rce

[N]


1HA400 pre-installed pile

loose sand

dense sand

Figure 3.42 1HA500 tests in dense and loose sand compared with the other monotonic tests

0

100

200

300

400

500

600

-10 -5 0

ho

rizo

nta

lfo

rce

[N]


1HA(500) driven pile in dense sand

30 N

40 N

50 N

100 N

200 N

300 N

500 N0

100

200

300

400

500

600

-20 -10 0

Ho

rizo

nta

lfo

rce[

N]

Horizontal displacement [mm]

1HA(500) driven pile in loose

sand

30 N

40 N

50 N

100 N

200 N

300 N

500 N



LABORATORY MODEL 80

3.5.1.2 Cyclic lateral behavior

3.5.1.2.1 Ratcheting

The ratcheting effect is defined as a gradual accumulation of permanent displacement in

granular material subjected to cyclic loads. When a cyclic load is applied to a foundation in

granular soil, for every cycle, there will be an accumulation of relative displacement whose

amplitude reduces with the number of cycles.

According to di Prisco (2012), strains can be described by the relation:

휀𝑖𝑗 = 휀𝑖𝑗𝑒𝑙 + 휀𝑖𝑗

𝑣𝑝 + 휀𝑖𝑗𝑐 + 휀𝑖𝑗

𝑟 (4.10)

Where the first term describes the elastic reversible response of the material for very small

strains while the second term describes the visco-plastic deformations. These two terms

control the standard cyclic response of the system and show that for small cycle amplitude,

no irreversible strains arise and the typical shake down response is observed (figure 3.43)

The third term of eq 4.10 controls the energy dissipation and the stiffness variation due to

cycling loads. Adding this parameter, it is possible to generalize the plastic ideal adaptation,

where no irreversible displacements are present (figure 3.44). The last term of the equation

describes the ratcheting phenomenon. 휀𝑖𝑗𝑟 and can characterize different behavior: it can

produce a progressive accumulation at constant velocity (figure 3.45 a), at decreasing

velocity (figure 3.45 b) or at increasing velocity (figure 3.45 c). In the case of granular soil,

a progressive stabilization occurs (case b).

Figure 3.43 Shake down response of the system, di Prisco (2012)



LABORATORY MODEL 81

Figure 3.45 (a) Constant velocity ratcheting, (b) progressive stabilization, (c) increment accumulation, di Prisco (2012)

Figure 3.44 Plastic ideal adaptation response, di Prisco (2012)



LABORATORY MODEL 82

3.5.1.2.2 Stabilization of accumulated displacement

In all the cyclic loading tests performed in this work, a stabilization of displacement

accumulation occurs as shown in figure 3.46.

To better understand the entity of such a stabilization, the ratio ∆𝑦𝑁

𝑦1 can be introduced where

𝑌1 is the relative displacement of the first cycle and ∆𝑦𝑁 is the difference between

displacement of two consecutive cycles (figure 3.47). Figure 3.48 and 3.49 show the

variation of this ratio with respect to the number of loads for loose and dense sand.

Test conducted at low horizontal forces, 30 N and 40 N have a more or less constant

horizontal trend, meaning that the response is always stable for any cycle. The amplitude of

the force provided is not sufficient to change the microstructure of the soil: energy is

completely dissipated without any evolution of the system. This can be interpreted as a sort

of steady-state condition for cyclic perturbations.

On the contrary, for large horizontal forces (50 N, 100 N, 200 N and 300 N,) a larger value

of the ∆𝑦𝑁

𝑦1 ratio is observed in the first cycle. Increasing the number of cycles, the ratio

decreases, finally reaching a plateau. In this case, the system is initially unstable because the

forces are able to change sand micro-structure: part of the energy is used to deform the soil.

Only after 6-8 cycles, the system tends to a stability condition where forces oscillate between

two constant values, dissipating all the energy with no further deformations.

0

50

100

150

200

250

300

350

-7 -6 -5 -4 -3 -2 -1 0

ho

rizo

nta

l fo

rce

[N]

hotizontal displacement [mm]

12HA300 dense sand

Figure 3.46 12HA500 test for dense sand



LABORATORY MODEL 83

Pre-installed piles tests (figure 3.50 and 3.51) were carried out just with large horizontal

loads, so it is not possible to compare the behavior of the system for small forces. Anyway,

results for larger horizontal loads confirms what is observed for driven piles. In this case,the

value of the ratio is one order of magnitude larger, probably due to the lower stability of the

system.

Figure 3.48 Relative displacement ∆𝑦𝑁

𝑦1 as a function of the number of cycles for driven pile in loose sand

-0,02

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0 2 4 6 8 10 12 14

∆yN

/y1

number of cycles


30 N

40 N

50 N

100 N

200 N

300 N

Figure 3.47 Relative displacement between two consecutive cycles (Giannakos,

Gazetas, 2002)



LABORATORY MODEL 84


𝑦1 as a function of the number of cycles for pre-installed pile in loose sand

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

0 2 4 6 8 10 12 14

∆yN

/y1

number of cycles

Pre-installed pile in loose sand

200

300

400

500

-0,4

-0,2

0

0,2

0,4

0,6

0,8

0 2 4 6 8 10 12 14

∆yN

/y1

number of cycles


30 N

40 N

50 N

100 N

200 N

300 N


𝑦1 as a function of the number of cycles for driven pile in dense sand



LABORATORY MODEL 85


𝑦1 as a function of the number of cycles for pre-installed pile in dense sand

Finally, the irreversible displacement at the end of every cycle is plotted as a function of the

number of cycles (figure 3.52).

Figure 3.52 Irreversible displacement (Giannakos, Gazetas, 2012)

Considering figures 3.53 and 3.54, it is possible to notice that, for every test, the irreversible

displacement increases with the increase of cycles number and with the increase of cycle

amplitude. Moreover, curves flatten as the number of cycles increases, witnessing the

tendency to stability of the system. As expected, final displacements are larger for smaller

relative density of the sand and for higher amplitude of the load.

These results were also obtained for pre-installed piles with much higher values or

irreversible displacements. (figure 3.55 and 3.56).

0

0,1

0,2

0,3

0,4

0,5

0,6

0 2 4 6 8 10 12 14

∆yN

/y1

number of cycles

Pre-installed pile in dense sand

200

300

400

500



LABORATORY MODEL 86

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14

final

dis

pla

cem

ent

[mm

]

number of cycles


30 N

40 N

50 N

100 N

200 N

300 N

0

1

2

3

4

5

0 2 4 6 8 10 12 14

final

dis

pla

cem

ent

[mm

]

number of cycles


30 N

40 N

50 N

100 N

200 N

300 N

Figure 3.53 Irreversible displacements for driven pile in loose sand

Figure 3.54 Irreversible displacements for driven pile in dense sand



LABORATORY MODEL 87

0

5

10

15

20

25

0 2 4 6 8 10 12 14

fin

al d

isp

lace

men

t [m

m]

number of cycles


200 N

300 N

400 N

500 N

Figure 3.55 Irreversible displacements for pre-installed pile in loose sand

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14

final

dis

pla

cem

ent

[mm

]

number of cycles

Pre-installed pile in dense sand

200 N

300 N

400 N

500 N

Figure 3.56 Irreversible displacements for pre-installed pile in dense sand



LABORATORY MODEL 88

3.5.1.2.3 Secant stiffness

The secant stiffness of the pile-soil system is defined as the ratio between the increment of

load and the increment of displacement (figure 3.57). The ratio between the stiffness at the

N-th cycle and the stiffness at the first cycle 𝐾𝑠𝑁

𝐾𝑠0 is plotted as a function of the number of

cycles for loose sand (figures 4.28) and dense sand (4.29). The resulting curves show an

abrupt increase after the first cycle and then they tend to a steady state.

For the same horizontal force, values of secant stiffness for loose sand are in general lower.

In both cases, tests conducted with forces of 30 N, 40 N and 50 N show larger values of 𝐾𝑠𝑁

𝐾𝑠0

ratio, while tests with 100 N, 200 N and 300 N of horizontal forces show much smaller

values of the ratio that remain almost constant after the first cycle.

For pre-installed pile the curves trend, shown in figure 3.60 and 3.61, is the same: an abrupt

increase after the first cycle and then a plateau. A correlation between amplitude of applied

force and variation of stiffness cannot be deducted. In this case lower horizontal forces were

not investigated.

These results seem inconsistent with the current guide lines for monopiles foundations where

it is suggested to introduce a degradation factor of static p -y curves to account for cyclic

loading. On the contrary, the result confirms an increase of stiffness with the number of

cycles as suggested by the work of LeBlanc et al. (2010a) (chapter 2.3).

Figure 3.57 Stiffness for different load cycles (Giannakos, Gazetas 2012)



LABORATORY MODEL 89

0

0,2

0,4

0,6

0,8

1

0 2 4 6 8 10 12 14

Ks N

/ K

s 0[k

N/m

m]

number of cycles


HA(30)

HA(40)

HA(50)

HA(100)

HA(200)

HA(300)

0

0,1

0,2

0,3

0,4

0,5

0,6

0 2 4 6 8 10 12 14

Ks N

/ K

s 0[k

N/m

m]

number of cycles


HA(30)

HA(40)

HA(50)

HA(100)

HA(200)

HA(300)

Figure 3.58 Variation of secant stiffness with number of cycles for driven pile in loose sand

Figure 3.59 Variation of secant stiffness with the number of cycles for driven pile in dense sand



LABORATORY MODEL 90

0

0,02

0,04

0,06

0,08

0,1

0,12

0 2 4 6 8 10 12 14

Ks N

/ K

s 0[k

N/m

m]

number of cycles


HA(200)

HA(300)

HA(400)

HA(500)

0

0,05

0,1

0,15

0,2

0 2 4 6 8 10 12 14

Ks N

/ K

s 0[k

N/m

m]

number of cycles

Pre installed pile in dense sand

HA(200)

HA(300)

HA(400)

HA(500)

Figure 3.60 Variation of secant stiffness with number of cycles for pre-installed pile in loose sand

Figure 3.61 Variation of secant stiffness with number of cycles for pre-installed pile in dense sand



LABORATORY MODEL 91

3.5.2 Pullout capacity

Figures 3.62 and 3.63 show the variation of the pullout capacity with respect to the maximum

lateral load applied during previous load cycles for loose and dense sand. Different curves

are plotted for different number of cycles.

In both cases the measured values are usually larger than simple pullout case and they are

higher for dense sand with respect to the loose one. However, no clear trends are identified

for the investigated number of cycles.

Considering results obtained for pre-installed piles (figures 3.64 and 3.65), much clear

correlations were found. Values of pullout resistance are larger than simple pull out case and

they are large for dense sand with respect to loose sand. Moreover, they usually increase

with the number of cycles and the amplitude of horizontal force.

So, in order to better investigate the behavior driven piles, 100 cycles tests with amplitude

of 200 N were performed for both loose and dense sand. The obtained results are depicted

in figure 3.66 and, for both cases, confirm that pullout force increases with the number of

cycles and it is larger in dense sand.

0

10

20

30

40

50

60

70

0 50 100 150 200 250 300 350

pull

out

forc

e [N

]

horizontal force [N]

Pullout resistance for driven pile in loose sand

1 cycle

6 cycles

12 cycles

simple pull-out

Figure 3.62 Pullout resistance for driven pile in loose sand as a function of horizontal force



LABORATORY MODEL 92

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300 350

pull

out

forc

e [N

]


Pullout resistance for driven pile in dense sand

1 cycle

6 cycles

12 cycles

simple pull-out

Figure 3.63 Pullout resistance for driven pile in dense sand as a function of horizontal force

0

20

40

60

80

100

120

140

0 100 200 300 400 500 600

pull

out

forc

e [N

]

horizontal force[N]

Pullout resistance for pre-installed pile in dense sand

1 cycle

6 cycles

12 cycles

simple pull out

Figure 3.64 Pullout resistance for pre-installed pile in dense sand as a function of horizontal force



LABORATORY MODEL 93

Considering the variation of the pullout force with the number of cycles for the same

amplitude of lateral load, as depicted in figures from 3.66 to 3.72, no general trends are

observed. The pullout force after cyclic lateral load is in general higher than simple pull out

(0 cycles), but it is not possible to draw a conclusion on how the number of cycles affects

the uplift resistance.

0

10

20

30

40

50

60

70

80

90

0 20 40 60 80 100 120

pull

out

forc

e[N

]

number of cycles

Pullout resistance for 200 N tests

Loose sand

Dense sand

simple pull out loose sand

simple pull out dense sand

Figure 3.65 Pullout resistance for 200 N test in loose and dense sand

0

5

10

15

20

25

30

35

40

45

50

0 100 200 300 400 500 600

pull

out

forc

e [N

]

horizontal force[N]

Pullout resistance for pre-installed pile in loose sand

1 cycle

6 cycles

12 cycles

simple pull-out

Figure 3.66 Pullout resistance for pre-installed pile in loose sand as a function of horizontal force



LABORATORY MODEL 94

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14

Pull

out

[N]

number of cycles

HA(40)

Loose sand

Dense sand

Figure 3.68 Pullout force as a function of the number of cycles for a maximum horizontal load of 40 N

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14

Pull

out

[N]

number of cycles

HA(30)

Loose sand

Dense sand




LABORATORY MODEL 95


0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14

Pull

out

[N]

number of cycles

HA(50)

Loose sand

Dense sand

0

10

20

30

40

50

60

0 2 4 6 8 10 12 14

Pull

out

[N]

number of cycles

HA(100)

Loose sand

Dense sand




LABORATORY MODEL 96

Figure 3.72 Pull out force as a function of the number of cycles for a maximum horizontal load of 200 N

0

5

10

15

20

25

30

35

40

45

50

0 2 4 6 8 10 12 14

Pull

out

[N]

number of cycles

HA(200)

Loose sand

Dense sand

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14

Pull

out

[N]

number of cycles

HA(300)

Loose sand

Dense sand




LABORATORY MODEL 97

3.6 Radial test

3.6.1 Interaction domains

Radial tests are performed imposing contemporary both horizontal and vertical tensile

forces. V/H ratios of 0.25, 0.5, 0.625, 0.75, 0.875 and 1 have been applied and just the case

of loose sand was investigated. The obtained values of pull out strength are listed in table

3.10. As expected, radial pull out forces are always higher than simple pullout and tend to

increase as the V/H ratio increases. For R(1), the maximum suitable forces of the

instrumentation was reached without the extraction of the pile, so it was not possible to

determine the real pullout capacity: just a lower bound can thus be estimated in this case.

Comparing these results with the one obtained for pre-installed pile (table 3.11), it is possible

to observe that, as expected, pullout forces are always larger in the case of driven pile for

every V/H ratio.

Table 3.10 Radial pullout forces for driven pile in loose sand

Test 𝑽𝑯⁄ VPULL [N]

R (0) 0 -32.052

R (0.25) 0,25 -41.741

R (0.5) 0.5 -86.802

R (0.625) 0.625 -102.608

R (0.75) 0.75 -156.998

R (0.875) 0.875 -341.319

R (1) 1 /



LABORATORY MODEL 98

Table 3.11 Radial pullout forces for pre-installed pile in loose sand

Test 𝑽𝑯⁄ VPULL [N]

R(0) 0 -14,257

R(0.25) 0,25 -16,457

R(0.5) 0.5 -27,757

R(0.625) 0.625 -50,757

R(0.75) 0.75 -89,657

R(0.875) 0.875 -121,257

Plot in figure 3.73 shows the part of the interaction failure domain obtained connecting all

the failure point of radial tests in the H/V plane. The resultant domain has not a convex

shape, as the minimum point capacity have been obtained by the simple pullout test. A

similar trend was observed in pre-installed pile as shown in figure 3.74.

The domain can be also reversed on the negative part of horizontal forces since the horizontal

response is independent on the direction of the lateral load.

As already explained, the employed loading apparatus has a limited capacity, so that it is

impossible to reach the failure point for every load path and correctly draw the entire domain.

Anyway, some compression tests have been performed so that also the positive part of V

axis have been investigated. Pure compression test, pure lateral load test and V/H ratios of

0.25, 0.375 and 0.5 tests have been performed. Failure was reached just for pure compression

load at 1692 N. For pure lateral load and R (0.5) tests the maximum extension capacity of

the horizontal piston was reached while for R (0.25) and R (0.375) tests, the maximum

capacity of the vertical load cell was attained without the failure of the system.

Also in this case the domain can be reversed on the negative part of H axis since the

horizontal response is independent on the direction of the horizontal load.



LABORATORY MODEL 99

The obtained interaction domain obtained with the results of radial tests is depicted in figure

3.75 where red points denote points where failure has been reached, while green points

denote point where failure has not been reached. The experimental interaction domain is

depicted in blue while the guessed failure domain in gray.

0

50

100

150

200

250

300

350

400

-400 -350 -300 -250 -200 -150 -100 -50 0

ho

rizo

nta

l fo

rce

[N]

vertical force [N]

Failure domain for driven pile in loose sand

failure domain

Figure 3.73 Failure domain for driven pile in loose sand

0

20

40

60

80

100

120

140

160

180

-140 -120 -100 -80 -60 -40 -20 0

ho

rizo

nta

l fo

rce

[N]

vertical force [N]

Failure domain for pre-installed pile in loose sand

failure domain

Figure 3.74 Failure domain for pre-installed pile in loose sand



LABORATORY MODEL 100

The obtained interaction domain has a concave butterfly shape. The minimum capacity is

obtained for pure vertical load both in compression and in tension. Compression resistance

is much higher with respect to tensile one so that the dominium is not symmetric with respect

to H axis.

As a lateral load is applied, the bearing capacity of the system increases. The higher is the

horizontal load, the higher is the vertical capacity.

As already explained in paragraph 3.5.1.1, when the pile moves horizontally, for high loads

(and displacements) the expansion lateral coefficient Kexp slightly decreases and reaches a

constant value, while the compression lateral coefficient Kcomp continuously increases. As a

result, the total earth pressure on the lateral surface of the pile increases and so does the shaft

resistance. The vertical capacity of the pile is enhanced.

For shallow foundation, the interaction domain is well known and has a convex shape. In

that case a horizontal load still causes an increment of lateral earth pressure, but at the same

time it also causes a mobilization of friction/adhesion at the soil-foundation base interface.

Due to the geometry of the problem (the base area is bigger than the lateral area), the

-1500

-1000

-500

0

500

1000

1500

-900 -400 100 600 1100 1600 2100 2600 3100H [

N]

V [N]

Interaction domain for driven pile in loose sand

guessed domainmeasured domainno failure pointfailure point

Figure 3.75 Interaction domain for driven pile in loose sand




reduction of the base resistance dominates the overall response of the system. An increase

in lateral load causes a reduction of the bearing capacity.

On the contrary, in rigid pile foundations, the increase of lateral shaft resistance

predominates with respect to the decrease of the base tip resistance. An increase in lateral

load enhances the bearing capacity of rigid pile foundation

3.6.2 Force-displacement evolution

An interesting fact can be noticed plotting vertical displacement as a function of vertical

force, as depicted in figure 3.76. Considering radial tensile tests, for the simple pull out case,

just one peak force is measured while, increasing the V/H ratio, curves present more relative

peaks. It is like sorts of “mini pull out” happen. The system reaches the failure, the pile starts

to move upward, and the applied vertical force starts to decrease because pistons are not able

to follow the load path since tests are carried out under load control. After a while, the

vertical force starts to increase again, and the velocity of movement decreases or stops up to

the following peak.

This beahvior is a clear demonstration that the failure domain has a butterfly shape. This

unstable response is caused by the distinctive inclination of the surface and the fact that the

employed loading paths reaches the domain tangentially.

As soon as the failure line is reached, the pile starts to move. The vertical force ceases to

increase. Meanwhile, the horizontal force continues in increasing. The load path in the H/V

plane moves up, in the safe side of the domain. Shaft resistance increases and a new stable

condition is reached. Then, tensile force restarts to grow and the load path restart to move to

the left untill the failure line is touched again and a new failure of the sistem is obtained.

In the simple pull out case, failure corresponds to the minimum point of the envelope. The

domain is reached ortogonally and an immediate failure is atteined.

The peculiarity of the aforementioned domain is further highlited when compared with a

convex domain. In fact, in case of the latter, load path attainnement of the envelope entails

an immediate and irreversible failure because an increase in horizontal load brings the load

path outside the safe zone into the unsafe one, as depicted in figure 3.77.




Since the pile is constrained in its head, also a bending moment arises, and the failure

envelope can be expanded in three dimensions. Unfortunately, it was not possible to

experimentally measure the bending moment. Anyway, it is worth noting that bending

moment is null during pure tensile or pure compression loads. On the contrary, the more the

horizontal load increases, the more the bending moment grows. Following this

consideration, it is expected a concave shape also on the moment direction.

-160

-140

-120

-100

-80

-60

-40

-20

0

0 5 10 15 20 25 30

ver

tica

l fo

rce

[N]


Pull out for radial tests

R (0.75)

R (0.625)

R (0.5)

R (0.375)

R (0.25)

simple pull out

R (0)

Figure 3.76 Pull out for radial tests in driven pile

Figure 3.77 Role of horizontal load in concave and convex domains



NUMERICAL ANALYSIS 103

4 NUMERICAL ANALYSIS

The finite element model will be described in the first part of the chapter, then, results

obtained by numerical model are discussed and compared with the one obtained by

laboratory test for simple pull-out, lateral load and lateral cyclic load.

4.1 The finite element model

As already explained in paragraph 3.4.3.3, for the employed dimension of pile and grains,

scale effects are negligible and sand can be considered as a continuum, so it is reasonable to

carry out the numerical analysis with a finite element model. The employed software is

Midas GTS NX.

Geometry of the numerical model is reproduced with the same measures of the laboratory

model. Since the problem is symmetric, just half of it is considered in order to save

computational time. Sand geometry has a depth of 400 mm and a thickness of 100 mm and

it is 870 mm long. Pile is 250 mm long and has a radius of 30 mm. The smaller pile screwed

to the foundation is reproduced with a height of 100 mm and a radius of 15 mm.

All geometry is discretized as a continuum through a hybrid mesh composed by tetrahedral

and hexahedral elements. Soil is discretized with a 0.02 m mesh that refines up to 0.005 m

near the pile. Pile is discretized with a 0.005 m mesh and smaller pile with a 0.02 m mesh.

between pile and soil a plane interface was introduced. The total number of elements is

33495 while nodes are 24766. Geometry and mesh discretization are shown in figure 4.1




The employed boundary conditions for the long lateral walls are rollers constraining

movements on y direction while, for smaller lateral walls, are rollers constraining

movements along x direction. The lower boundary of the soil is constrained along all the

three directions while the surface is unconstrained. During lateral loads, in order to avoid

pile’s rotation due to the presence of the sleeve, rollers constraining z direction are applied

to the top part of the smaller pile. During pull out test this constrain is removed.

Pile and smaller pile are modeled with an isotropic elastic constitutive law with an elastic

modulus E= 200000000 kN/m2, a Poisson’ s ratio ν= 0.25 and a unit weight of 78 kN/m3.

The soil behavior is assumed to be governed by an elastic perfectly-plastic constitutive

relation based on the non-associated Mohr–Coulomb criterion with friction angle ϕ=35°,

cohesion c=0.1 kN/m2 and a dilatancy angle of 12°. In order to find the elastic modulus, a

calibration process was carried out. Since it is not possible to reproduce the driving

procedure with numerical tools, the FE model results are compared with experimental results

for pre-installed piles. The best match between numerical and experimental results is found

for an elastic modulus E =1150 kN/m2 for dense sand and E =750 kN/m2 for loose sand. The

adopted unit weight of the soil is γ= 16 kN/m3 and the Poisson’ s ratio ν=0.3.

Plane interface non-linearity is modeled with Coulomb friction where structural parameters

are modeled with literature values that suggest using the value of the elastic modulus

Figure 4.1 Geometry and mesh discretization




increased of two orders of magnitude, so for instance, for dense sand, normal stiffness

modulus kn=115000 kN/m3 and tangential stiffness modulus kt=115000 kN/m3. The adopted

friction angle between sand and steel pile is 20°, as suggested by Viggiani (1999). The

adopted dilatancy angle is 5° while cohesion and tensile strength are assumed to be null.

4.2 Numerical simple pullout

A load controlled simple pullout test in dense sand is simulated applying a 100 N tensile

force on the head of the smaller pile through 100 increments.

Before applying the force, three construction stages are employed. In the first one, the mesh,

boundary conditions and self-weight of the soil are introduced. Then, self-weight of the pile

is initialized trough five increments and finally interface is activated. This process of

splitting the initial part of mesh initialization in different stages is strictly necessary. In fact,

pile self-weight is much larger than sand one. The pile tends to sink, and if its load is not

applied in different steps, a distortion of the mesh and convergence problems can arise.

On the other hand, this process afflicts test results, Extraction force must overcome also the

tangential forces generated due to pile sinking after steel weight initialization. As observed

in figure 4.2, the tensile force that brings the pile to the initial position corresponds to 22.4

N. Subtracting this mesh initialization force to the graph, it is obtained the real pull out curve.

A comparison between the numerical curve and the experimental one is shown in figure 4.3.

A good agreement in terms of final vertical displacement and pull out forces are obtained.

The value of pull out force for the pre-installed pile in dense sand is 18.67 N while the pullout

force of the model is 19.5 N.

Anyway, a different trend is observed: while the experimental test shows zero displacement

up to 15 N and then an abrupt step followed by a plateau, numerical simulation depicts a

monotonic trend.




Figure 4.3 Comparison between numerical and experimental pull out

-25

-20

-15

-10

-5

0

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

ver

tica

l fo

rce

[N]


Numerical Vs experimental pullout

Experimental pull out

Numerical pull out

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

-0,2 -0,1 0,0 0,1 0,2 0,3 0,4

ver

tica

l fo

rce

[N]


Numerical simple pullout test

Figure 4.2 Numerical simple pull out test




4.3 Lateral loading test

The mesh initialization procedure is the same of the simple pull out case. Then, a horizontal

force of 200 N in x direction is applied to the pile through 20 load increments and then it is

removed, still with 20 load increments. The simulation is repeated for both loose and dense

sand. Results of the simulation are displayed in figure 4.4 where they are also compared with

experimental results of pre-installed piles.

It is possible to observe that there is a good matching of peaks and residual displacements

between numerical and experimental curves. Anyway, while empirical curves present the

typical two inflections discussed in paragraph 4.2.1, numerical curves show a monotonic

behavior. In fact, the employed elastic-perfectly plastic isotropic model cannot capture the

variation of stiffness during the loading phase of the material, neither in compression nor in

extension. An anisotropic hardening law should be employed.

0

50

100

150

200

250

-7 -6 -5 -4 -3 -2 -1 0

ho

rizo

nta

l fo

rce

[N]


Numerical vs empirical results for 1HA200 test

empirical, loose sand

empirical, dense sand

numerical, loose sand

numerical, dense sand

Figure 4.4 Comparison between numerical and empirical results for 1HA200 test




Displacements of the soil are shown in figure 4.5. The smaller pile and the applied load are

shown, while the pile is omitted to allow a better visualization of soil movements, As

expected, the maximum displacements are near the pile head along x direction in the zone

of sand that contrast the movement of the pile. It is clear the formation of two lobes upstream

and downstream the pile that spreads from the pile tip to the surface with different inclination

angles. This confirms what has been said in paragraph 4.2.1.1: for monopile foundations, the

deep mechanism does not come into play. Just the superficial mechanism arises, and the pile

behaves like a sheet pile. Values of soil displacement along x direction when the pile is

subjected to the peak force of 200 N are shown in figure 4.6.

Figure 4.6 Total displacement of the soil

Figure 4.5 Values of displacement for 200N horizontal load along x direction [mm]




Another interesting aspect that can be investigated is the distribution of stresses. Horizontal

stresses along x direction increase with depth and reach the maximum value in front of the

pile tip downward the pile.

Knowing the value of the soil stresses along x direction, it is possible to find a rough

estimation of compression and extension thrusts acting on the pile. The half pile is divided

along y direction in two identical quarters of cylinder. Horizontal stresses acting on the x

direction of the downstream quarter are integrated over the area and the passive thrust is

obtained. In the same way, horizontal stresses acting on the x direction of the upstream

quarter are integrated, and the active thrust is obtained. Repeating the procedure for all the

load increments, it is possible to find the evolution of extension and compression thrusts

with the displacement of the pile, as depicted in figure 4.8. The at-rest thrust of the soil is

approximately 10 N. Then, as expected, extension thrust rapidly decreases and after 1 mm

reaches a constant value of about 3 N. On the contrary, compression thrust initially increases

at a slower rate with respect to extension thrust and then continuously increases up to 70 N

without reaching a plateau.

These results confirm what is observed in paragraph 4.2.1.1. When subjected to lateral load,

the monopile foundation just develops the superficial mechanism. The extension thrust

rapidly decreases while compression thrust increases at a slower rate. The difference

between the increasing and decreasing rate causes a variation on the applied force and the

double inflection is observed

Figure 4.7 Maximum soil stress for 200N horizontal load along x direction, [N/mm2]




0

10

20

30

40

50

60

70

80

0 1 2 3 4 5

forc

e [N

]

displacement[mm]

Expansion and compression thrust

Expansion thrust

Compression thrust

Figure 4.8 Expansion and compression thrust trends



CONCLUSIONS 111

5 CONCLUSIONS

The aim of the present work is to experimentally and numerically investigate the behaviour

of rigid monopile foundations subjected to simple pullout forces, pullout forces after

horizontal cyclic loads and radial forces.

Thanks to the simple pullout test results, it was proved that the uplift force is higher in dense

sand with respect to loose sand and for driven piles with respect to pre-installed piles,

showing that the relative density and the installation technique have a key role on the tensile

resistance of the pile.

Then, thanks to the pullout tests after horizontal cyclic loads , the lateral behavior of the pile

and the variation of tensile resistance were investigated. From load/displacement curves it

was possible to observe a double inflection trend. When subjected to lateral loads, monopile

foundations do not develop the characteristic deep mechanism of long piles so that they

behave like sheet piles with an upstream zone in extension and a downstream zone in

compression. During lateral cyclic load a stabilization of displacement accumulation occurs,

and the stiffness of the soil-pile system tends to increase. Moreover, the previous cyclic

horizontal load history has a positive impact on the tensile resistance of the pile. After the

application of lateral cyclic load, the pullout forces always increase with respect to the simple

pullout case. However, a general correlation between tensile force and number and

amplitude of cycles was not found.

Performing radial tests, it was possible to draw the interaction domain of the pile. Contrary

to what is observed for shallow foundation, the failure envelope shows a concave shape. Due

to the geometry of the problem, the increase of lateral shaft resistance dominates the overall

response of the foundation system. An increase of lateral load causes an increment in the

vertical resistance of the pile both in compression and in tension.

Finally, a numerical model was developed, and some tests were carried out. For simple

pullout, a good matching between numerical and experimental tensile resistance was

obtained. Concerning lateral loads, also in this case a good matching between numerical and

experimental results was found. The double inflection trend was not detected probably due

to the too simplistic constitutive laws of the software. Anyway, the deformed shape of the



CONCLUSIONS 112

model clearly shows the presence of the expansion and extension wedges without the

development of the deep mechanism as observed in experimental results. Moreover,

integrating the horizontal stresses acting on the pile wall, the extension and compression

thrusts trend was recovered.

It can be concluded that the worst scenario for a rigid monopile foundation is the simple

pullout case and any addition of monotonic, cyclic or radial horizontal load leads to an

increase on the uplift capacity of the pile.

As regards the future developments, the behaviour of the monopile should be also studied

for different kinds of soil, as silt and clay. Furthermore, more powerful laboratory equipment

should be employed in order to investigate the pile behaviour after a high number of

horizontal load cycles and high amplitudes of horizontal force. Also radial tests should be

performed with more powerful laboratory equipment and with the possibility of measuring

the acting bending moment in order to correctly draw the complete interaction domain.

Furthermore, the obtained results should be also validated with software able to employ

anisotropic hardening constitutive laws. Finally, all the tests should be repeated with a

different pile constraint, able to allow pile rotation and having zero bending moment in the

pile head.



Appendix A: experimental results 113

Appendix A: experimental results

Simple pullout test

Simple Pullout

Pile type Sand type Measured force [N] Pullout force [N]






-40

-35

-30

-25

-20

-15

-10

-5

0

0 0,5 1 1,5 2 2,5 3

ver

tica

l fo

rce

[N]


Simple pullout test

Loose sand

Dense sand




Pullout after lateral cyclic load

0

50

100

150

200

250

300

350

-4,5 -4 -3,5 -3 -2,5 -2 -1,5 -1 -0,5 0

ho

rizo

nta

l fo

rce

[N]


1 cycle dense sand

300 N

200 N

100 N

50 N

40 N

30 N

0

50

100

150

200

250

300

350

-7 -6 -5 -4 -3 -2 -1 0

ho

rizo

nta

l fo

rce

[N]


6 cycles dense sand

300 N

200 N

100 N

50 N

40 N

30 N

0

50

100

150

200

250

300

350

-7 -6 -5 -4 -3 -2 -1 0

ho

rizo

nta

l fo

rce

[N]]


12 cycles dense sand

300 N

200 N

100 N

50 N

40 N

30 N




0

50

100

150

200

250

300

350

-16 -14 -12 -10 -8 -6 -4 -2 0

ho

rizo

nta

l fo

rce

[N]


6 cycles loose sand

300 N

200 N

100 N

50 N

40 N

30 N

0

50

100

150

200

250

300

350

-18 -16 -14 -12 -10 -8 -6 -4 -2 0

ho

rizo

nta

l fo

rce

[N]


12 cycles loose sand

300 N

200 N

100 N

50 N

40 N

30 N

0

50

100

150

200

250

300

350

-14 -12 -10 -8 -6 -4 -2 0

ho

rizo

nta

l fo

rce

[N]


1 cycle loose sand

300 N

200 N

100 N

50 N

40 N

30 N




0

5

10

15

20

25

30

35

-0,5 -0,4 -0,3 -0,2 -0,1 0

ho

rizo

nta

l fo

rce

[N]


1HA30 driven pile

Loose sand

Dense sand

0

5

10

15

20

25

30

35

-0,6 -0,5 -0,4 -0,3 -0,2 -0,1 0

ho

rizo

nta

l fo

rce

[N]


6HA30 driven pile

Loose sand

Dense sand

0

5

10

15

20

25

30

35

-0,6 -0,5 -0,4 -0,3 -0,2 -0,1 0

ho

rizo

nta

l fo

rce

[N]


12HA30 driven pile

Loose sand

Dense sand




0

5

10

15

20

25

30

35

40

45

-0,8 -0,7 -0,6 -0,5 -0,4 -0,3 -0,2 -0,1 0

ho

rizo

nta

l fo

rce

[N]


1HA40 driven pile

Loose sand

Dense sand

0

5

10

15

20

25

30

35

40

45

50

-0,8 -0,7 -0,6 -0,5 -0,4 -0,3 -0,2 -0,1 0

ho

rizo

nta

l fo

rce[

N]


6HA40 driven pile

Loose sand

Dense sand

0

5

10

15

20

25

30

35

40

45

50

-0,8 -0,7 -0,6 -0,5 -0,4 -0,3 -0,2 -0,1 0

ho

rizo

nta

l fo

rce

[N]


12HA40 driven pile

Loose sand

Dense sand




0

10

20

30

40

50

60

-1,8 -1,6 -1,4 -1,2 -1 -0,8 -0,6 -0,4 -0,2 0

ho

rizo

nta

l fo

rce

[N]


1HA50 driven pile

Loose sand

Dense sand

0

10

20

30

40

50

60

-2,5 -2 -1,5 -1 -0,5 0

ho

rizo

nta

l fo

rce

[N]


6HA50 driven pile

Loose sand

Dense sand

0

10

20

30

40

50

60

-2,5 -2 -1,5 -1 -0,5 0

forz

a o

rizz

onta

le [

N]


12HA50 driven pile

Loose sand

Dense sand




0

20

40

60

80

100

120

-5 -4 -3 -2 -1 0

ho

rizo

nta

l fo

rce

[N]

horizontal force [mm]

1HA100 driven pile

Loose sand

Dense sand

0

20

40

60

80

100

120

-7 -6 -5 -4 -3 -2 -1 0

ho

rizo

nta

l fo

rce

[N]


6HA100 driven pile

Loose sand

Dense sand

0

20

40

60

80

100

120

-7 -6 -5 -4 -3 -2 -1 0

ho

rizo

nta

l fo

rce

[N]


12HA100 driven pile

Loose sand

Dense sand




0

50

100

150

200

250

-12 -10 -8 -6 -4 -2 0

forz

a o

rizz

onta

le [

N]

horizontal force [mm]

1HA200 driven pile

Loose sand"

Dense sand"

0

50

100

150

200

250

-12 -10 -8 -6 -4 -2 0

ho

rizo

nta

l fo

rce

[N]


6HA200 palo battuto

Loose sand

Dense sand

0

50

100

150

200

250

-14 -12 -10 -8 -6 -4 -2 0

ho

rizo

nta

l fo

rce

[N]


12HA200 driven pile

Loose sand

Dense sand




0

50

100

150

200

250

300

350

-14 -12 -10 -8 -6 -4 -2 0

ho

rizo

nta

l fo

rce

[N]


1HA300 driven pile

Loose sand"

Dense sand

0

50

100

150

200

250

300

350

-16 -14 -12 -10 -8 -6 -4 -2 0

ho

rizo

nta

l fo

rce

[N]


6HA300 driven pile

Loose sand

Dense sand

0

50

100

150

200

250

300

350

-18 -16 -14 -12 -10 -8 -6 -4 -2 0

ho

rizo

nta

l fo

rce

[N]


12HA300 driven pile

Loose sand

Dense sand





n. of cycles Horizontal force [N] Measured force [N] Pullout force [N]

(no self-weight)

1 30 106.1 42.4

1 40 95.9 32.2

1 50 97.2 33.5

1 100 97.1 33.4

1 200 98.3 34.6

1 300 91.2 27.5

1 500 105 41.3

6 30 105.4 41.7

6 40 96.7 33.0

6 50 94 30.3

6 100 101.4 37.7

6 200 103.7 40

6 300 109.1 45.4

12 30 97.2 33.5

12 40 98 34.3

12 50 96.7 33

12 100 105.1 41.4

12 200 100.6 36.9

12 300 123.3 59.6

100 200 119.9 56.2





n. of cycles Horizontal force [N] Measured force [N] Pullout force [N]

(no self-weight)

1 30 132.7 68.9

1 40 119.4 55.7

1 50 113.0 49.3

1 100 106.8 43.1

1 200 104.2 40.5

1 300 97.0 33.3

1 500 121.7 58.0

6 30 124.4 60.7

6 40 116.4 52.6

6 50 111.1 47.4

6 100 103.1 39.4

6 200 98.1 34.3

6 300 98.1 34.3

12 30 114.7 51.0

12 40 153.7 90.0

12 50 110.0 46.3

12 100 110.0 46.3

12 200 109.8 46.0

12 300 119.9 56.2

100 200 142.2 78.4




0

10

20

30

40

50

60

70

0 50 100 150 200 250 300 350

pull

out

forc

e [N

]


Pullout resistance for driven pile in loose sand

1 cycle

6 cycles

12 cycles

simple pull-out

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300 350

pull

out

forc

e [N

]


Pullout resistance for driven pile in dense sand

1 cycle

6 cycles

12 cycles

simple pull-out




0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14

Pull

out

[N]

number of cycles

HA(30)

Loose sand

Dense sand

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14

Pull

out

[N]

number of cycles

HA(50)

Loose sand

Dense sand

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14

Pull

out

[N]

number of cycles

HA(40)

Loose sand

Dense sand




0

10

20

30

40

50

60

0 2 4 6 8 10 12 14

Pull

out

[N]

number of cycles

HA(100)

Loose sand

Dense sand

0

5

10

15

20

25

30

35

40

45

50

0 2 4 6 8 10 12 14

Pull

out

[N]

number of cycles

HA(200)

Loose sand

Dense sand

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14

Pull

out

[N]

number of cycles

HA(300)

Loose sand

Dense sand




Radial tests results

Tensile radial tests

Test Failure Horizontal force [N] Vertical force [N]

R(0) 0 -32.05

R(0.25) 26.98 -41.47

R(0.5) 75.26 -86.8

R(0.625) 105.55 -102.61

R(0.75) 166.12 -156.99

R(0.875) 353.03 -341.319

R(1) 763.74 -700

Lateral 580 0

Compression radial tests

Test Failure Horizontal force [N] Vertical force [N]

R(0) 0 1691.77

R(0.25) 490 2023.12

R(1) 726.37 2023.2

Lateral 668.88 733.66



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