Mass displacement due to pile installation in soft and sensitive clay The influence pile installation with precast concrete displacement piles has on adjacent areas Master’s Thesis in the Master’s Programme Infrastructure and Environmental Engineering GILA EDVARDSSON PAULA MELIN-NYHOLM Department of Architecture and Civil Engineering Division of Geology and Geotechnics Geotechnical Engineering Research Group CHALMERS UNIVERSITY OF TECHNOLOGY Master’s Thesis ACEX30-18-31 Gothenburg, Sweden 2018 Master’s Thesis ACEX30-18-31 Mass displacement due to pile installation in soft and sensitive clay The influence pile installation with precast concrete displacement piles has on adjacent areas Master’s Thesis in the Master’s Programme Infrastructure and Environmental Engineering GILA EDVARDSSON PAULA MELIN-NYHOLM Department of Architecture and Civil Engineering Division of Geology and Geotechnics Geotechnical Engineering Research Group Chalmers University of Technology Göteborg, Sweden 2018 Mass displacement due to pile installation in soft and sensitive clay The influence pile installation with precast concrete displacement piles has on adjacent areas Master’s Thesis in the Master’s Programme Infrastructure and Environmental Engineering GILA EDVARDSSON PAULA MELIN-NYHOLM © GILA EDVARDSSON, PAULA MELIN-NYHOLM, 2018 Examensarbete ACEX30-18-31 Institutionen för arkitektur och samhällsbyggnadsteknik Chalmers tekniska högskola, 2018 Department of Architecture and Civil Engineering Division of Geology and Geotechnics Geotechnical Engineering Research Group Chalmers University of Technology SE-412 96 Göteborg Sweden Telephone: +46 (0)31-772 1000 Cover: Plane strain model in PLAXIS, where the cross section 475+480 of the project Västlänken Station Centralen is modelled. The illustration shows the total displace- ment around and in the excavation, for more information see Chapter 5. Göteborg, Sweden, 2018 Mass displacement due to pile installation in soft and sensitive clay The influence pile installation with precast concrete displacement piles has on adjacent areas Master’s Thesis in the Master’s Programme Infrastructure and Environmental Engineering GILA EDVARDSSON PAULA MELIN-NYHOLM Department of Architecture and Civil Engineering Division of Geology and Geotechnics Geotechnical Engineering Research Group Chalmers University of Technology Abstract The installation of displacement piles is known to lead to disturbances in soft sen- sitive clays as found in Gothenburg, i.e. deformations, excess pore water pressures and loss of strength and stiffness. In this Thesis the mass displacement and pore pressure build up due to installation of precast concrete displacement piles is in- vestigated for the construction of the Central Station project within Västlänken. A numerical plane strain cavity expansion approach is adopted using a 2D Finite Element code with a suitable constitutive model for soft soils. The modelling ap- proach was first validated against field measurements from nearby projects, i.e., a bridge support for the Partihallsbron and a project on the lowering of the highway E45 between Lilla Bommen and Marieholm before the Västlänken case is studied in detail. The results indicate that for a well calibrated model the trends and magnitudes of the vertical component of the mass displacements can be obtained with a maximum error of approximately 10 millimetres. Over time the initial settlements double in magnitude due to consolidation and creep. The location and construction sequence of the piling works was further investigated for the Västlänken case by simulating pile installation before and after excavation of the building pit and with or without pre-augering. For these scenarios the maximum vertical mass displacement of the ground surface was largest when piling after construction of the retaining walls and excavation, but the impact area was smallest. The lowest vertical mass displacement occurred when a pre-augering/pile-block was used. Adjacent support structures that confined the piled soil volume deformed due to the mass displacement from pile installation. Furthermore, the excess pore pressure was largest adjacent close to the cavity directly after piling, with an excess pore water front moving outwards during consolidation over a total period of 80 years. Keywords: Mass displacement, superpile, prescribed line displacement, pile instal- lation, PLAXIS 2D. i Massundanträngning som en följd av installation av pålar i lös och känslig lera Påverkan som pålinstallation med färdiggjutna betongpålar har på närliggande områden Examensarbete inom masterprogrammet Infrastruktur och Miljöteknik GILA EDVARDSSON PAULA MELIN-NYHOLM Institutionen för Arkitektur och Samhällsbyggnadsteknik Avdelningen för Geologi och Geoteknik Forskargruppen för Teknisk Geologi och Geoteknik Chalmers Tekniska Högskola Sammanfattning Vid pålning av massundanträngande pålar i lös och känslig lera, som den i Göteborg, är kända för att orsaka störningar i jorden. I examensarbetet är massundanträngnin- gen och uppbyggnaden av porvattentrycket som en konsekvens av pålning av färdig- gjutna massundanträngande betongpålar, för konstruktionen av Västlänken Station Centralen undersökt. Detta med numerisk modellering, PLAXIS 2D, plane strain antagande, superpåle och en tolkning av Cavity Expansion Method. Den odräner- ade responsen av jorden var modellerad med den konstitutiva modellen Soft Soil och långtidsfallet med Soft Soil Creep. Modellen validerades mot fältdata från andra byggprojekt i området, närmare bestämt ett av brostöden till Partihalls- bron och nedsänkningen av E45:an, mellan Lilla Bommen och Marieholm. Mod- ellen skapades för att fånga den nuvarande stresshistoriken, sättningshastigheten och porvattenövertrycket i området. Pålningen modellerades som en ihålighet fylld med ett poröst linjär-elastiskt material, vilket expanderade med en föreskriven lin- jeförskjuten. Härledd från en ekvation som gav den procentuella ökningen av super- pålen, med antagandet att leran ej skulle genomgå någon volymförändring, då den i princip är ogenomsläpplig. Resultatet visade att modellen fångade trenden och stor- leken på massundanträngningen, med felvärden på maximalt tio millimeter. Beträf- fande långtidssättningarna gav modellen, med hänsyn till krypning, nästan dubbelt så höga sättningar vid 80 års konsolidering. Effekten på massundanträngning och uppbyggnaden av porvattenövertryck beroende på var pålinstallationen skedde un- dersöktes i Västlänken, då med pålning från schaktbotten eller innan schaktningen utfördes, med eller utan knektning eller dragning av lerproppar. Slutsatsen var att den maximala hävningen av markytan skedde då pålningen utfördes från schaktbot- ten, men påverkningsområdet var minst. Den lägsta hävningen gavs då lerproppar drogs eller knektning utfördes. Intilliggande stödkonstruktioner deformerades som en konsekvens av massundanträngnigen. Porvattenövertrycket var direkt efter pål- ningen som högst intill superpålen och vandrade sedan till de horisontella gränserna under konsolideringen och hade efter 80 år konsoliderat bort. Nyckelord: Massundanträngning, superpåle, föreskriven linjeförskjuten, pålinstalla- tion, PLAXIS 2D. ii Acknowledgements This Master’s Thesis was conducted at the Division of Geology and Geotechnics at Chalmers University of Technology and in collaboration with Tyréns. The Thesis was written between February and June 2018. Firstly would we like to thank our supervisor Tim Björkman at Tyréns for all the help, knowledge and encouragement throughout the work with this Master’s The- sis. We would also like to thank Jelke Dijkstra, our supervisor and examiner at Chalmers, for your honest opinions and advices. Further would we like to thank Tara Wood for your expertise and all the colleagues at Tyréns for the help. Finally, would we like to thank our families and friends for their support during this process. Gila Edvardsson and Paula Melin-Nyholm, Gothenburg, June 2018 iii Contents List of Figures vii List of Tables xi 1 Introduction 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Pile installation and its effect on surrounding soil 5 2.1 Pile types and installation techniques . . . . . . . . . . . . . . . . . . 7 2.2 Soil mechanics interpreted with constitutive models . . . . . . . . . . 8 2.3 Empirical and analytical calculation methods . . . . . . . . . . . . . 10 2.3.1 Rhenman’s method . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.2 Shallow Strain Path Method and Cavity Expansion Method . 12 2.4 Numerical calculation methods . . . . . . . . . . . . . . . . . . . . . 14 3 Prediction of mass displacement due to pile installation, using PLAXIS 2D 17 3.1 Investigation and chosen modelling technique . . . . . . . . . . . . . . 17 3.2 Deriving model parameters . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2.1 Study site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2.2 Pre-consolidation pressure . . . . . . . . . . . . . . . . . . . . 20 3.2.3 Poisson’s ratio for loading and unloading . . . . . . . . . . . . 20 3.2.4 Modified compression, swelling and creep index . . . . . . . . 21 3.3 Construction of Base Model in PLAXIS 2D . . . . . . . . . . . . . . 21 3.3.1 Calculation of prescribed line displacement . . . . . . . . . . . 23 3.3.2 Calculation phases . . . . . . . . . . . . . . . . . . . . . . . . 25 4 Validation of model and modelling technique 27 4.1 Field measurements and project information from Partihallsbron and E45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.2 Calculations of Partihallsbron and E45 . . . . . . . . . . . . . . . . . 30 4.3 Validation of model parameters and prescribed line displacement . . . 32 4.4 Validation of model behaviour with focus on strains . . . . . . . . . . 39 4.5 Partihallsbron and E45 - Result and analysis . . . . . . . . . . . . . . 41 v Contents 4.6 Partihallsbron and E45 - Discussion . . . . . . . . . . . . . . . . . . . 48 5 Case study - Västlänken Station Centralen 51 5.1 Västlänken - Calculations . . . . . . . . . . . . . . . . . . . . . . . . 53 5.2 Västlänken - Result and analysis . . . . . . . . . . . . . . . . . . . . . 56 6 Conclusion and further investigations 63 A Derived model parameters I B Validation of model and modelling technique XI C Case study - Västlänken Central Station XXV vi List of Figures 1.1 Illustration over Västlänken with the area around the Central Station marked with a rectangle, modified from [Trafikverket, 2014]. . . . . . . 2 1.2 Illustration over the construction projects taking place around the Central Station in Gothenburg, modified from [Google Maps, 2018]. . . 3 2.1 Schematic illustration over a shallow foundation to the left and a deep foundation to the right, modified from [Viggiani et al., 2014]. . . . . . 5 2.2 Illustration of the phases that occurring during pile history, from left to right; installation, equalisation and loading, modified from [Ottolini et al., 2014]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Schematic illustration showing to the left a floating pile and to the right an end bearing pile. . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 The Mohr-Coulomb failure criterion, defined as the failure envelop and the principal stresses defining the Mohr-Coulomb circle. . . . . . 9 2.5 SSC model, the NCS illustrating the boundary between small and large strains. The Mohr-Coulomb failure criterion is illustrated through the MMC line, with permission from [Karstunen and Amavasai, 2017]. . . 10 2.6 Prediction of mass displacement of the ground surface with Rhenman’s method, modified from [Hintze et al., 1997]. . . . . . . . . . . . . . . . 11 2.7 Conceptual model for SSPM representing the three steps used to simu- late a single pile penetration, modified from [Sagaseta and Whittle, 2001] 12 2.8 Cavity with inner and outer pressure, Pi and Pu respectively, and the inner, outer and plastic radius denoted r1, r2 and r3 respectively. . . . 14 2.9 Difference between a plane strain model, to the left, and an axisym- metric model, to the right, both on a Cartesian coordinate system, modified from [PLAXIS, 2018a]. . . . . . . . . . . . . . . . . . . . . . 15 3.1 Map over the area around Gothenburg Central Station, inside the cir- cle, in 1790, to the left and in 1890 to the right. After the fill of dredged material was placed, modified from [Ramböll AB et al., 2015]. 19 3.2 Logarithmic relation between εv and p′, giving the values for λ∗ and κ∗. 21 3.3 Schematic illustration over the chosen soil profile in the Base Model. 22 3.4 The Base Model in PLAXIS 2D. . . . . . . . . . . . . . . . . . . . . 23 3.5 Schematic illustration over a general piling area, seen from above. . . 24 3.6 Excess pore pressures in the Base Model during the control year. . . . 26 vii List of Figures 4.1 Schematic illustration over the piling area for Partihallsbron and the location from where the field measurements were retrieved, modified from [Edstam, 2011]. . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.2 Illustration over E45, where the dots inside the circle are installed piles. The circle marks the chosen section and the points A-F the location from where the field measurements were retrieved, modified from [Trafikverket, 2018]. . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.3 Resulting vertical mass displacement for the high-, low- and original line displacement, and field measurements for Partihallsbron, Sce- nario 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.4 Result from IL Oedometer test performed on a sample from 8 metres depth in laboratory and simulated in PLAXIS SoilTest. . . . . . . . . 35 4.5 Result from Triaxial compression test performed in laboratory on a sample from the depth 11 metres and simulated in PLAXIS SoilTest. With both the original κ∗, κ∗1, and the new derived κ∗2. . . . . . . . . 36 4.6 Resulting vertical mass displacement for κ∗1, κ∗2 and the field measure- ments for Partihallsbron, Scenario 1. . . . . . . . . . . . . . . . . . . 37 4.7 Resulting vertical mass displacement on the ground surface with κ∗1 and κ∗2, compared with the field measurements for E45 in Point F, Scenario 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.8 The vertical mass displacement for the three scenarios, for Partihalls- bron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.9 The vertical mass displacement of the ground surface, for the three scenarios in Point F, E45. . . . . . . . . . . . . . . . . . . . . . . . . 42 4.10 Excess pore pressure distribution with distance from the superpile, with consideration to depth, directly after piling, for Partihallsbron, Scenario 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.11 Excess pore pressure distribution ten metres from the superpile in Par- tihallsbron, Scenario 1. On different levels with consideration to time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.12 The excess pore pressure distribution on the level of -15 metres in the model, with consideration to time and distance from superpile, for Partihallsbron Scenario 1. . . . . . . . . . . . . . . . . . . . . . . . . 47 5.1 Blue print over a part of Västlänken Station Centralen, retrieved from tender documents. The section investigated is marked with a rectan- gle, modified from [Andersson, 2018a]. . . . . . . . . . . . . . . . . . 51 5.2 Blue print over the cross section 475+480, retrieved from tender doc- uments. The section investigated is marked with a rectangle, modified from [Andersson, 2018b]. . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.3 Model in PLAXIS after the excavation was carried out. . . . . . . . . 53 5.4 Vertical mass displacement directly after the last pile installation phase for Västlänken, Model 1. . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.5 Horizontal mass displacement directly after the last pile installation phase for Västlänken, Model 1. . . . . . . . . . . . . . . . . . . . . . 58 viii List of Figures 5.6 Excess pore pressure directly after the last pile installation phase for Västlänken, Model 1. . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.7 Excess pore pressure after 80 years of consolidation for Västlänken, Model 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.8 Excess pore pressure after 80 years of consolidation with a load acting on the excavation bottom, for Västlänken, Model 2. . . . . . . . . . . 61 A.1 Plot of effective vertical stress and pre-consolidation pressure. . . . . III A.2 Interpolation of κ∗ from IL Oedometer test samples on the depths 8, 15, 19 and 45 metres. . . . . . . . . . . . . . . . . . . . . . . . . . . . IV A.3 Interpolation of κ∗ from IL Oedometer test samples on the depths 8, 15, 19 and 45 metres, for the first 10 metres. . . . . . . . . . . . . . . V A.4 Interpolation of λ∗ from IL Oedometer test samples on the depths 8, 15, 19 and 45 metres . . . . . . . . . . . . . . . . . . . . . . . . . . . VI A.5 Interpolation of λ∗ from IL Oedometer test samples on the depths 8, 15, 19 and 45 metres, for the first 10 metres. . . . . . . . . . . . . . . VII A.6 Interpolation of λ∗ from IL Oedometer test samples on the depths 8, 15, 19 and 45 metres, for the last 79.5 metres. . . . . . . . . . . . . . VIII A.7 Pore pressure distribution in the area around Gothenburg Central Sta- tion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX B.1 Evaluation of the prescribed line displacements influence on the hor- izontal mass displacement, in the project Partihallsbron, Scenario 1. . XI B.2 Parameter evaluation of vur on the horizontal mass displacement in the project Partihallsbron, Scenario 1. . . . . . . . . . . . . . . . . . . XII B.3 Parameter evaluation of κ∗ on the vertical mass displacement in the project Partihallsbron, Scenario 1. . . . . . . . . . . . . . . . . . . . . XIII B.4 Parameter evaluation of κ∗ on the horizontal mass displacement in the project Partihallsbron, Scenario 1. . . . . . . . . . . . . . . . . . . XIV B.5 Result from IL Oedometer test performed on a sample from 15 metres depth in laboratory and simulated in PLAXIS SoilTest. . . . . . . . . XV B.6 Result from IL Oedometer test performed in laboratory on a sample from 19 metres depth and simulated in PLAXIS SoilTest. . . . . . . XVI B.7 Result from IL Oedometer test performed on a sample from 45 metres depth in laboratory and simulated in PLAXIS SoilTest. . . . . . . . . XVII B.8 Result from Triaxial compression test performed in laboratory and simulated in PLAXIS SoilTest. With both κ∗1 and κ∗2. . . . . . . . . . XVIII B.9 Result from Triaxial compression test performed in laboratory and simulated in PLAXIS SoilTest, with only κ∗1. . . . . . . . . . . . . . . XIX B.10 Resulting horizontal mass displacement for κ∗1, κ∗2 and the field mea- surements in the project Partihallsbron. . . . . . . . . . . . . . . . . . XX B.11 The horizontal mass displacement for Scenario 1, Scenario 2, Sce- nario 3 and field measurements, Partihallsbron. . . . . . . . . . . . . XXI B.12 The vertical mass displacement of the ground surface in Point B, for the project E45. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXII B.13 The vertical mass displacement of the ground surface in Point D, for the project E45. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXIII ix List of Figures C.1 Vertical mass displacement directly after the last piling phase for Västlänken, Model 2. . . . . . . . . . . . . . . . . . . . . . . . . . . XXVI C.2 Vertical mass displacement directly after the last piling phase for Västlänken, Model 3. . . . . . . . . . . . . . . . . . . . . . . . . . . XXVII C.3 Horizontal mass displacement directly after the last piling phase for Västlänken, Model 2. . . . . . . . . . . . . . . . . . . . . . . . . . . XXVIII C.4 Horizontal mass displacement directly after the last piling phase for Västlänken, Model 3. . . . . . . . . . . . . . . . . . . . . . . . . . . XXIX C.5 Excess pore pressure directly after the last piling phase for Västlänken, Model 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXX C.6 Excess pore pressure after 80 years of consolidation for Västlänken, Model 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXXI C.7 Excess pore pressure directly after the last piling phase for Västlänken, Model 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXXII C.8 Excess pore pressure after 80 years of consolidation for Västlänken, Model 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXXIII x List of Tables 3.1 Calculation phases used in the Base Model. . . . . . . . . . . . . . . . 25 4.1 Prescribed line displacement for Partihallsbron. . . . . . . . . . . . . 30 4.2 Prescribed line displacement for E45. . . . . . . . . . . . . . . . . . . 30 4.3 The calculation phases used in Partihallsbron, Scenario 1. . . . . . . 31 4.4 The calculation phases used in E45, Scenario 1. . . . . . . . . . . . . 31 4.5 Calculation phases used in Partihallsbron, for Scenario 2 and Sce- nario 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.6 Calculation phases used in E45, for Scenario 2 and Scenario 3. . . . . 32 5.1 Calculation phases used in the case study, Västlänken Station Centralen. 54 5.2 Prescribed line displacement for Västlänken Station Centralen. . . . . 55 A.1 Model parameters derived and used in the modelling of fill and moraine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I A.2 Model parameters derived and used in the modelling of the clay. . . . II C.1 Model properties for the support structures used for Västlänken [Wood, 2017].XXV C.2 Model properties for the stamps used for Västlänken [Wood, 2017]. . . XXV xi Notations Roman upper case letters E ′ Effective Young’s modulus E ′oed Constrained modulus G Shear modulus K0 Earth pressure coefficient at rest KNC 0 Earth pressure coefficient for normally consolidated soils MMC Modified Mohr-Coulomb Pi Inner pressure acting on a spherical cavity Pu Outer pressure acting on the spherical cavity Rinter Interface factor S Point source S’ Mirror image sink Vp Pile volume Roman lower case letters asp Area of superpile apa Piling area b Width of the piling area c′ Effective cohesion cref Reference cohesion d Depth of the pile below the ground surface or excavation bottom einit Initial void ratio kx Horizontal permeability in PLAXIS ky Vertical permeability in PLAXIS l Length of the piling area p′ Mean effective stress r Radius v′ Poisson’s ratio for drained conditions vur Poisson’s ratio for loading and unloading wsp Width of superpile x Mass displacement within the piling area xmax Maximum horizontal boundary in PLAXIS xmin Minimum horizontal boundary in PLAXIS ymax Maximum vertical boundary in PLAXIS ymin Minimum vertical boundary in PLAXIS Greek letters α Relative weight of constructions in Rehnman β Relative weight of constructions in Rehnman γ Relative weight of constructions in Rehnman γs Deviatoric strain γsat Saturated unit weight γunsat Unsaturated unit weight δ Relative weight of constructions in Rehnman ∆Vpr Volume of removed clay with pre-augering ε1 Axial strain εv Volumetric strain η The heave factor κ∗1 Modified swelling index in PLAXIS κ∗2 Modified swelling index in PLAXIS κ∗ Modified swelling index λ∗ Modified compression index µ∗ Modified creep index σ′c Pre-consolidation pressure σ′v Effective vertical stress φ′c Effective friction angle ψ Dilatancy angel Abbreviations CEM Cavity expansion method CRS Constant rate of strain FEM Finite element method IL Incremental loading LE Linear elastic MC Mohr-Coloumb NCS Normal compression surface OCR Over consolidation ratio POP Pre-overburden pressure SPM Strain path method SS Soft Soil SSC Soft Soil Creep SSPM Shallow strain path method xiv "It is not the beauty of a building you should look at; it’s the construction of the foundation that will stand the test of time." - David Allan Coen 1 Introduction A global trend and contemporary challenge is growing urbanisation, which puts pres- sure on already densely populated areas. The cities must grow and space effective solutions need to be utilised to cope with the increasing demand on housing and infrastructure. As a global challenge this is highly relevant, not least in Sweden, as the population in South West of Sweden is growing rapidly. Therefore, an infras- tructural investment is made with the city of Gothenburg as hub, called Västsvenska Paketet [Västsvenska paketet, nda]. The investment incorporates several infrastruc- tural investments such as highways, railroads, bridges and commuting traffic. This to ensure more reliable transport for industry, smaller environmental impact and better commuting options. The aim is to make the city more accessible to everyone who wants to work or study in Gothenburg and enable the city to grow by making the commuting more efficient. To enable these infrastructural projects, the need for a stable and efficient foun- dation method is crucial. One of the most common foundation methods, with the purpose to transmit the loads from the constructions down in the sub-layers with adequate strength, is the pile [Knappett and Craig, 2012]. Piles are often used when constructing bridge approach abutments, road embankments and buildings on soft and sensitive soil. One soft soil type is the sensitive clay that in large parts of Scan- dinavia can be found along coastlines and near lakes, areas which are commonly densely populated [Massarsch and Wersäll, 2013]. Hence, prone to have large and heavy constructions, which is the case in Gothenburg. The installation of piles in such areas can result in horizontal and vertical mass displacement of the soil, de- pending on the used pile type and piling technique. Investigations and predictions of mass displacement and the influence it has on adjacent constructions can be carried out with several different methods, such as empirical, analytical and numerical. The different calculation methods have their advantages and disadvantages, where the complexity of the problem and the level of accuracy needed to be obtained decides which method is most appropriate. Meth- ods based on empirical relationships often give rough predictions, whereas semi- analytical and analytical methods give better predictions and a higher level of ac- curacy. Numerical methods such as the finite element method is commonly used for modelling geotechnical problems when deformations are of importance. 1 1. Introduction 1.1 Background The biggest individual investment in Västsvenska Paketet is Västlänken, an eight kilometres long double tracked railway, which mainly is going to be constructed as a tunnel under the central parts of Gothenburg, see Figure 1.1. Three stations will be constructed underground, one besides the existing Central Station, one at the junction Korsvägen and one in the district of Haga [Västsvenska paketet, ndb]. Both commuter trains and regional trains will traffic the railway which will link together the railway system in the South West of Sweden. Figure 1.1: Illustration over Västlänken with the area around the Central Station marked with a rectangle, modified from [Trafikverket, 2014]. In addition to Västlänken being constructed adjacent to the existing Central Station, are several other infrastructural projects constructed constructed, projected for the area. A number of them as part of theVästsvenska paketet [Västsvenska paketet, nda]. A new bridge, Hisingsbron, is constructed to replace the old bridge Götaälvbron and connect Hisingen with the main land, see Figure 1.2. Adjacent to this is the highway E45 is to be lowered, a stretch of 900 metres between Lilla Bommen and Marieholm, where approximate half of the stretch will be built as a tunnel, see Fig- ure 1.2 [Sabattini and Wallgren, 2018]. Between the lowering of the highway E45 and Hisingsbron, a part of the new city district, Platinan, will be constructed. 2 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 1. Introduction The city district is planned to emerge around the Central Station through construc- tion of new housing, business premises and offices, and is called Centralenområdet [Västsvenska paketet, ndc]. Another large construction being built as part of Cen- tralenområdet, is the building Regionens Hus, which is built alongside the lowering of the highway E45, see Figure 1.2. Figure 1.2: Illustration over the construction projects taking place around the Cen- tral Station in Gothenburg, modified from [Google Maps, 2018]. As the city of Gothenburg is partly located on deep deposits of soft and sensitive clay it is crucial to consider and execute good foundations which can control the rate and occurrence of settlements. The chosen foundation method is, to a large extent, precast concrete piles which is classified as a displacement pile, due to the consequently mass displacement that occurs when installing them. Thus, it is prob- lematic when a large number of piles are driven in a confined area, in a number of parallel projects with different contractors. Therefore, in the area around Gothen- burgs Central Station the contractors have started a project group where consultants from the projects discuss the movements and measures that should be taken, called Project Navet. This has enabled the contractors to take part of each other’s field measurements of the mass displacement, among other things. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 3 1. Introduction 1.2 Aim The aim of the Master’s Thesis is to investigate numerical methods to predict the magnitude of mass displacement, as a consequence of pile installation with precast concrete displacement piles. The focus is on a case study of Västlänken Station Centralen. The aim is divided into the following objectives: • Evaluate the derived model parameters, with consideration to parameters which influence the result most. • Derive and evaluate an equation for the prescribed line displacement, which is based on the area of the piles being installed. • Perform numerical calculations on the chosen projects with PLAXIS 2D. • Compare the result with field measurements and analyse the differences. • Compare numerical models with or without consideration to time dependent behaviour such as creep, and analyse how this influence the result. • Investigate how the excess pore pressure varies in the model with consideration to time and distance to the piling area. • Compare the difference in the resulting mass displacement, when installing the piles from the ground surface with or without pre-augering/pile block or from the excavation bottom. 1.3 Limitations In the Thesis is not the whole pile installation modelled, instead is the installation modelled as the expansion of a filled cavity in soft and sensitive clay. Ignoring the penetration of the pile into the soil, and other soil types. 1.4 Scope The Thesis investigates the horizontal and vertical mass displacement occurring due to the installation of precast concrete displacement piles in three projects; Par- tihallsbron, the lowering of the highway E45 and Västlänken Station Centralen. Considering how the influence pile area, installation technique and the geometry from which the piles are going to be installed have on adjacent areas. The calcu- lations are carried out numerical with the finite element method, PLAXIS 2D and the constitutive models Mohr-Coulomb, Soft Soil and Soft Soil Creep. Furthermore, investigations are carried out concerning the change in excess pore water pressure, the influence creep have on long term settlements and how the deviatoric strains are captured in the model. 4 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 2 Pile installation and its effect on surrounding soil There are two types of foundations, shallow foundations and deep foundations, see Figure 2.1. The latter is the foundation type considered in this Thesis. The char- acteristics of a deep foundation is that it consists of elements extending to a large depth into the ground, whilst occupying a small area in the plan. The most common version of this, hence deep foundation, is the pile [Knappett and Craig, 2012]. Figure 2.1: Schematic illustration over a shallow foundation to the left and a deep foundation to the right, modified from [Viggiani et al., 2014]. Physical processes occur in connection to the pile during its lifetime, which can be divided into the three phases: installation, equalisation and loading, see Figure 2.2 [Ottolini et al., 2014]. During the installation phase will large strains, mass displacement, soil disturbance and excess pore water pressure occur consequently to the rapid change in void ratio and stresses in the soil [Abu-Farsakh et al., 2015]. When the pile penetrates the soil, the soil below the pile toe will be pushed downward, and then moved horizontally. Therefore, the initial soil structure and stress history will be destroyed. For nearly impermeable clays, during undrained conditions, will there be almost no volume change. Hence, the pile volume driven will correlate to the volume of mass displace- ment. During the pile installation in undrained conditions will the pore pressure in the soil change as soft clays contracts with no volume change. Which directly influence the total stresses in the soil [Randolph et al., 2011]. 5 2. Pile installation and its effect on surrounding soil 6 CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-16-50 remoulding and disturbance of the soil around the tip of the pile (Randolph et al., 1979). The equalization phase is governed by consolidation around the pile, due to a dissipation of the excess pore pressure and the change of mean effective stress. In the loading phase the load of the pile head is transmitted to the soil. Figure 2.2 A schematic figure of the physical processes during pile driving history (Ottolini et al., 2014). 2.1.3 Effects on adjacent piles Pre-existing piles in the ground affect the magnitude of the displacements for a driven pile. The existing pile acts as a reinforcement and counteracts the displacements, especially the heave. The heave is instead concentrated closer to the driven pile. The existing pile itself is also effected and heaves but is also moved with the displacement in lateral direction (Massarsch, 1976). The behaviour could be seen in Figure 2.3. Figure 2.3 Effects of the adjacent pre-installed pile when driving a pile into soil (Wersäll and Massarsch, 2013). Figure 2.2: Illustration of the phases that occurring during pile history, from left to right; installation, equalisation and loading, modified from [Ottolini et al., 2014]. Following the installation phase is the equalisation phase, also called the set-up period, where the soil moves back towards the pile due to dissipation of the ex- cess pore pressures induced, consolidation, and the rearrangement of soil particles, thixotropic effects [Abu-Farsakh et al., 2015]. The equalisation of pore pressure, creep and thixotropic effects means that the bearing capacity of the soil starts to re- cover [Augustesen et al., 2006]. The time it takes for the bearing capacity to recover, called the set-up period, is dependent on the hydraulic conductivity and stiffness of the clay. In Gothenburg clay is the empirical knowledge that the equalisation time is between three to six months [Fellenius, 1972]. Adjacent to the pile shaft will the decrease of void ratio in the clay lead to an increase of the undrained shear strength. In the following loading phase is the load on the pile head transmitted through the pile into the soil. Where the bearing capacity of the pile is directly proportional to the interface friction angle at the pile-soil interface and the normal effective stresses [Randolph et al., 2011]. 6 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 2. Pile installation and its effect on surrounding soil 2.1 Pile types and installation techniques Different piles and piling techniques will have different effect on the mass displace- ment [Knappett and Craig, 2012]. Mass displacement occurs when the volume of piles installed pushes away corresponding volume of soil [Olsson and Holm, 1993]. To counteract mass displacement can soil be removed through drilling, decreasing the total volume of soil which is being pushed away, commonly known as pre-augering. Piles can be installed through several techniques; a simple division is driven piles or bored piles [Fleming et al., 2008]. The choice of piling method depends on the soils characteristics, groundwater conditions, the consequences the mass displace- ment could have etcetera. Driven piles can further be divided into dropping weight, explosive, vibration and jacking against a reaction. The dropping weight, more com- monly known as a drop hammer, is the traditional method of pile driving. The pile is driven through the soil by striking the pile head. Bored piles, also known as drilled piles, is installed by using rotary augering machines, and therefore causes no mass displacement as the soil is removed. When the piles cutting level is beneath ground surface, hence the pile head is out of reach from the piling machine, can a pile-block be used [Olsson and Holm, 1993]. A pile-block is an extension with the approximate same area as the pile head, which enables the machine to continue driving the pile to its intended cutting level. When the pile is installed the pile-block will be drawn back up, leaving a cavity, which the soil can fall back into, decreasing the moved soil volume. Figure 2.3: Schematic illustration showing to the left a floating pile and to the right an end bearing pile. Piles can be made of materials such as concrete, steel and wood [Fleming et al., 2008]. Further, can piles be divided into displacement or non-displacement piles, where the former is piles with a large cross sectional area, and the latter have smaller cross sectional areas or hollow cross sections. Therefore, causing less mass displacement when installed. The chosen pile type in the Thesis is precast concrete piles, which is a displacement pile, and the most common pile type in Sweden [Edstam, 2011]. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 7 2. Pile installation and its effect on surrounding soil Furthermore, piles can be end bearing or floating, see Figure 2.3. End bearing piles are installed with the toe of the pile either on solid bedrock or in a stiff soil layer with adequate strength. Floating piles relies on the adhesion between the soil and the pile shaft. Depending on the soil type can the adhesion be friction or cohesion. In this Thesis floating cohesion piles are investigated. 2.2 Soil mechanics interpreted with constitutive models Soil is a complex material as it is compounded of three individual materials; grains, water and air in the voids [Lade, 2005]. Thus, when subjected to stress and stress change, e.g. pile installation, the soil will show highly non-linear, anisotropic and time dependent behaviour [Knappett and Craig, 2012]. To capture this behaviour, different constitutive soil models can be used, which will lead to different degrees of accuracy, depending on the model. The concept of a constitutive model is to describe the soil mechanics through a set of equations which give the relationship between stress and strain in a single element [Lade, 2005]. The more accurate a model captures the soil mechanics, the complexity increases, as well as the number of input model parameters. The field data of the soil is often limited and retrieved through basic field test; hence, the data is often too insufficient to select all the parameters needed for the more advanced models. The simplest constitutive models assume that the soil behaves linear-elastic, only showing reversible deformations, therefore, implying that the soil is infinitely strong. The applied shear strain is directly proportional to the applied shear stress [Knappett and Craig, 2012]. For total stress, the relationship between stress and strain is given by Hooke’s law. However, soil is a highly non-linear function of shear strain and effective confining stress. To be able to model the failure of the soil the Mohr-Coulomb failure criterion can be applied, which is based on that the soil is a frictional material exposed to three dimensional states of stress. The Mohr-Coloumb (MC) model can also be called the linear elastic perfectly plastic model, as the soil is assumed to be elastic until it reaches a defined failure condition, illustrated by when the Mohr circle touches the failure envelop in one point in the plane, see Figure 2.4. Thus, only experi- ence reversible deformations and no irreversible deformations before failure. So, in some numerical models a yield function can be introduced that models the plastic deformations for the model [PLAXIS, 2017a]. However, in soil there is not elastic and plastic deformations, only a small span of reversible deformations and then ir- reversible deformations. But, as much of the theories and the constitutive models is built on the simplification of elastic and plastic deformations is these terms used in the Thesis. Furthermore, to capture the undrained response of the soil, which is a necessity when looking at the short-term response of soft clays, must the model be adapted, as the shear strength of the soil is different with comparison to drained 8 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 2. Pile installation and its effect on surrounding soil conditions which the model is based on. The undrained behaviour is further de- fined with a friction angle (φ′) of one, which means that the shear strength should be constant in an undrained soil [Knappett and Craig, 2012]. This could lead to inaccurate predictions of the soils strength. The model further fails to capture the softening or hardening of the soil after it has reached its peak strength. Figure 2.4: The Mohr-Coulomb failure criterion, defined as the failure envelop and the principal stresses defining the Mohr-Coulomb circle. Two additional models which adapts the Mohr-Coulomb failure criterion are the Soft Soil (SS) model and Soft Soil Creep (SSC) model. Where both models adapt an isotropic assumption, which many of the constitutive models do with the hydraulic conductivity. Whilst, soil in reality is anisotropic as no soil consist of perfectly spherical grains. The SSC model further aims to capture the secondary consoli- dation, creep, and is a development of the SS model. Both models consider the elastic and plastic deformations of the soil, reversible and irreversible deformations, in contrast to the MC model. The models further work with non-linear elasticity in contrast to MC. Besides the creep is the main difference between the models, the way they interpret the yield surface, the boundary between small strains and large strains. Were in SSC has the yield surface been replaced with a Normal Com- pression Surface (NCS), see Figure 2.5 [Karstunen and Amavasai, 2017]. The NCS boundary in SSC is falsely assumed to be the contour of constant volumetric creep, thus have the drawback of reproducing unrealistic creep strains for nearly all stress paths [Olsson, 2013]. Another drawback with the SSC model is how the (false) creep is modelled, as it models non-plausible excess pore pressures. Which in turn will influence other processes in the model. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 9 2. Pile installation and its effect on surrounding soil 14 The size of NCS to the current stress surface (CSS), i.e. the ratio of p’eq/p’p, in Eq. (3), is a triaxial equivalent of the inverse of OCR (vertical overconsolidation ratio). The model, therefore, predicts creep strains both in the normally consolidated and the overconsolidated region. The consequence of the formulation in Eq. (4) is that if the creep rate when the soil is normally consolidated is a, as indicated in Figure 6, it is significantly smaller in overconsolidated state, given the exponent β has typically a rather large value. Similarly to the Soft Soil model, the stress states above the Mohr Coulomb failure condition (noted with MMC in Figure 6) are not allowed, and hence the model is not suitable for highly overconsolidated clays. Figure 6. Soft Soil Creep model. Figure 7. Definition of the modified creep index. pp′ q p´ ce = a� eq pNCS: p p′ ′= ce a� << eqp′ CSS ac v =ε� ac v <<ε� MCM *M a) Definition of µ* t (ln –scale) εp µ* b) Linking of µ* to Cα t (log10 –scale ) e Cα )1(3.2 * e Cα + =µ Figure 2.5: SSC model, the NCS illustrating the boundary between small and large strains. The Mohr-Coulomb failure criterion is illustrated through the MMC line, with permission from [Karstunen and Amavasai, 2017]. 2.3 Empirical and analytical calculation methods To calculate and predict the soil behaviour due to pile installation, e.g mass dis- placement, as the increase in excess pore pressure and strain response, can empirical, analytical and numerical calculation methods be used. 2.3.1 Rhenman’s method Empirical calculations rely on patterns observed in the field and laboratory, and so, do not account for the small variations that can occur. Giving rough predictions as best. One empirical calculation method which is used for the calculation of mass displacement is Rhenman’s method. The method contains several simplifications and assumptions. The method is based on the assumption that the vertical mass displacement of the ground surface occurs within an area of one pile length away from the piling area, see Figure 2.6 [Hintze et al., 1997]. Other assumptions are that the ground surface is horizontal and that the volume of vertical mass displacement is proportional to the volume of the piles installed. The vertical mass displacement of the ground surface is calculated through Equation 2.1. 10 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 2. Pile installation and its effect on surrounding soil x = η(Vp − ∆Vpr) d[(α + β)( l 2 + d 3) + (γ + δ)( b 2 + d 3) + bl d ] (2.1) Where: x = Mass displacement within the piling area d = Depth of the pile below the ground surface or excavation bottom b = Width of the piling area l = Length of the piling area η = Heave factor, ranging between 0.5 to 1.0, often 0.75 Vp = Pile volume ∆Vpr = Volume of removed clay with pre-augering α, β, γ, δ = Relative weight of constructions A, B, C and D, The calculation method only considers the mass displacement of the ground surface. The model is built on volumetric ratios and geometry, ignoring the soil behaviour. Thus, the method is useful if a fast and rough prediction of the mass displacement of the ground surface is sought. But if information on additional processes in the soil and a higher accuracy is sought the method cannot be used. Figure 2.6: Prediction of mass displacement of the ground surface with Rhenman’s method, modified from [Hintze et al., 1997]. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 11 2. Pile installation and its effect on surrounding soil 2.3.2 Shallow Strain Path Method and Cavity Expansion Method Different analytic methods can be used to model and predict the mass displace- ment and soil disturbance due to piling, e.g. cavity expension method (CEM) and the strain path method (SPM). One semi-analytical method based on SPM is the Sagaseta’s method, which can be referred to as the shallow strain path method (SSPM) [Sagaseta and Whittle, 2001]. SPM assumes that the soil deformations and strains occurring due to deep pile installation in undrained clays is independent of the shear strength. The method further model the mass displacement that occur due to the irrational flow of an ideal fluid. Although, this assumption ignores that dif- ferent soils can have highly different penetration resistance and soil stresses. Field observations, tests and empiric knowledge shows a link between pile driving and ground heave, whereas SPM analysis of pile penetration calculates that all soil ele- ments undergo a net downward movement. Thereof, is SPM suitable for calculating strains near the pile toe, but not for far field conditions where the ground surface can affect the soil deformations. These limitations are addressed in the SSPM analysis through the incorporation of the effects from a stress free ground surface. 56 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2001 FIG. 1. Geometry and Notation Used in SSPM Analyses FIG. 2. Conceptual Model for SSPM: (a) SSPMRepresentation of Shallow Penetration Problem; (b) Equivalent Solution (Steps 1 ! 2 ! 3) tion caissons used to anchor offshore tension leg platforms (Andersen et al. 1993). To address these limitations, the SSPM explicitly includes the effects of the stress-free ground surface following the ap- proach first proposed by Sagaseta (1987). In the SSPM method (Fig. 2), the pile can be represented by superimposing full- space solutions for a point source S and mirror image sink S! (i.e., absorbing an equal and opposite volume to the source) at some embedment depth h below and above the notional ground surface, respectively. At points along the ground sur- face, the combined action of the source and sink will cancel out the normal stresses but will double the shear stresses. To simulate a stress-free surface, corrective shear tractions (Fig. 2, Step 3) are applied to the surface. This involves evaluating the shear strains due to the source and image sink and the corresponding shear stresses occurring at the ground surface (assuming a given stress-strain behavior for the soil). The strains due to these corrective shear tractions are then added to the previous fields due to the source and virtual sink. In contrast to the source and sink solutions, the calculation of corrective shear tractions requires a specific stress-strain relation for the soil. Analytical solutions are only possible for linear, elastic behavior. In this case, the resulting deformations are inversely proportional to the soil modulus, and the correc- tive stresses themselves are computed using the same soil modulus. Hence, the soil modulus will cancel out and the re- sulting deformations are independent of the assumed elastic properties. Nevertheless, the solution for this component of the deformation is based on the assumption of homogeneous, lin- ear, isotropic behavior. This type of framework has previously been applied to the analysis of ground movements caused by tunneling (Sagaseta 1987; Uriel and Sagaseta 1989; Verruijt and Booker 1996), pipe jacking (Rogers and O’Reilly 1991; Chapman 1993), and pile driving (Sagaseta 1987; Chow and Teh 1990). However, in all of these cases, the analyses were formulated in small strains, considering only the final state of deformation. The current incarnation of the SSPM incorporates large strains by formulating in terms of the velocities of soil elements rather than their displacements. The resulting velocities (and strain rates) due to the source, image sink, and corrective shear trac- tions can then be integrated numerically (i.e., considering the changes in geometry) along the particle paths as the pile pen- etrates from the stress-free ground surface. In this approach, the consideration of large strains is only partial, as deforma- tions associated with the corrective shear tractions are still ob- tained from small-strain elastic solutions. However, the solu- tion is a good approximation, because the contributions from the source and virtual sink are far more important than the corrective shear tractions in the region near the source (where large strains are of concern). At some distance from the pile, the assumption of small strains becomes a good approximation and closed-form ex- pressions can be derived for the ground displacements in some cases. Table 1 summarizes these small-strain solutions (de- noted by subscript ss) including complete deformation fields J. Geotech. Geoenviron. Eng., 2001, 127(1): 55-66 D ow nl oa de d fr om a sc el ib ra ry .o rg b y C ha lm er s U ni ve rs ity o f T ec hn ol og y on 0 2/ 20 /1 8. C op yr ig ht A SC E. F or p er so na l u se o nl y; a ll rig ht s r es er ve d. Figure 2.7: Conceptual model for SSPM representing the three steps used to sim- ulate a single pile penetration, modified from [Sagaseta and Whittle, 2001] . 12 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 2. Pile installation and its effect on surrounding soil Mass displacement is calculated in four steps with SSPM. The installation of a single pile is simulated in three steps, see Figure 2.7. The result from these simulations is then combined for a final analysis of the mass displacement. The first step, see Figure 2.7, entails the assumption of a point source (S), which penetrates the soil throughout the pile length [Sagaseta and Whittle, 2001]. S is thought to discharge an ideal fluid throughout the penetration. Thus, creating a spherical flow which causes the mass displacement. The presence of a ground surface is ignored and the soil is assumed to be in-compressible. In the second step is a mirror image sink (S’) introduced, which moves in the opposite direction, see Figure 2.7. Cancelling out the normal stresses, whilst the shear stress doubles. Hence, do not corresponds to an unloaded ground surface. To counteract this is a set of corrective radial shear forces added in step three, see Figure 2.7. The method works for predictions with floating cohesion piles in deep deposits of clay, which the method was designed for but cannot be applied for end bearing piles or floating cohesion piles which are driven close to the bedrock, as the displacements will behave differently [Sagaseta and Whittle, 2001]. CEM studies the soil’s reaction to pile installation, i.e. excess pore pressure, change in stresses and mass displacement, through the use of an expanding or contracting cylindrical cavity, instead of an ideal fluid as in SPM and SSPM [Yu, 2013]. The method was first introduced from research on copper, where it was concluded that deep penetrations lead to large strains and consequently hardening of the material [Bishop et al., 1945]. There are several approaches when using the CEM, as the spherical or cylindrical cavity can be modelled with constitutive models such as linear elastic (LE), elastic-perfectly plastic or strain hardening/softening plasticity. When using LE models the soil will be modelled to have infinite strength. Whereas, the elastic-perfectly plastic models will have constant strength during both the load- ing and unloading [Yu, 2013]. Therefore, do not consider the variation of the soil’s strength due to deformation history. As pile installation is a rapid process, and the low permeability of soft clays, is the undrained response of the soil modelled. The solution in LE, isotropic models, is often to assume that the inner (Pi) and outer (Pu) pressure acting on the sphere or cavity starts from zero, see Figure 2.8. Where the soils deformations occur purely plastic. For the elastic-perfectly plastic models a yield surface is introduced, often Trescas, von Mises or Mohr-Coulomb depending on if it is cohesion or friction soil, and a plastic radius, see Figure 2.8. As the soil first will behave elastic due to the initial pressure, before initial yielding occurs at the cavity wall leading to plastic deformations around the inner cavity wall and increased Pi, see Figure 2.8, [Yu, 2013]. To fully capture the behaviour and the influence from softening/hardening due to strains these kind of constitutive models should be applied. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 13 2. Pile installation and its effect on surrounding soil Figure 2.8: Cavity with inner and outer pressure, Pi and Pu respectively, and the inner, outer and plastic radius denoted r1, r2 and r3 respectively. Both the CEM, SPM and SSPM can be applied with numerical methods, which is a necessity when more advanced constitutive material models are used, due to the complexity of the problem. 2.4 Numerical calculation methods There are several numerical calculation methods which in combination with constitu- tive soil models can be used to predict the response of the soil due to pile installation. Numerical calculation methods are characterised by the discretization of continua and the use of algorithms; which allows for calculation of non-linear and time depen- dent material behaviour, arbitrary geometries, initial or in situ conditions, multi- phase media, different types of loading i.e. static and cyclic loading, and the impact of environmental factors, i.e. temperature and fluids [Desai and Gioda, 1990]. Thus, can numerical modelling be used for geotechnical problems, such as pile installation and mass displacement, that can be complex to solve by using empirical or analytic methods. There are several numerical methods that can be used for these prob- lems such as the finite element method, boundary element method, discrete element method and finite difference method. The finite element method (FEM) solves differential equations approximately where complex problems are divided into several finite elements. These elements are then approximated separately, but in relation to each other [Ottosen and Petersson, 1992]. Hence, can the approximation of these elements be assembled to a complete system, thus the solution for the unit. Two FEM-based software programs that can be used for the modelling of geotechnical problems, such as mass displacement, are PLAXIS 2D and PLAXIS 3D. 14 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 2. Pile installation and its effect on surrounding soil Furthermore, analytical calculations can be adapted with numerical methods, such as SPM and CEM. The latter have been adopted with FEM in different scientific re- ports and research. In the report Numerical simulations of stone column installation is the FEM based software program PLAXIS used [Castro and Karstunen, 2010]. Whereas, in the report Evaluating pile installation and subsequent thixotropic and consolidation effects on setup by numerical simulation for full-scale pile load tests is the FE based software programme Abaqus used [Abu-Farsakh et al., 2015]. In PLAXIS 2D either a plane strain or an axisymmetric model can be used. The dif- ferent approaches have different advantages and disadvantages. The main difference between the two models is the geometry, where the plane strain assumption should be used for models with a uniform cross section, where the stress state and loading scheme is fairly constant for a significant length perpendicular to the cross section, i.e. roads [PLAXIS, 2018a]. When it comes to the strains and displacements in the perpendicular direction, the z-direction, they are assumed to be zero, whereas the normal stress is still accounted for. The axisymmetric model is instead used for cir- cular structures, where the radial cross section is uniformed. The deformation and stress state are assumed to be equal around the central axis. In the axisymmetric model is the x-coordinate the radius and the y-coordinate the axial line of symme- try, hence no negative x-coordinates. The difference of the plane strain model and axisymmetric model can be seen in Figure 2.9. Figure 2.9: Difference between a plane strain model, to the left, and an axisym- metric model, to the right, both on a Cartesian coordinate system, modified from [PLAXIS, 2018a]. Both models have their advantages and disadvantages when modelling pile instal- lation. One disadvantage with the plane strain model is that it will model a piling area which is constant in the z-direction. Thereof, entails that the pile will become an infinity long wall if the pile is modelled as a soil polygon/cluster. However, in an axisymmetric model can only one pile be modelled. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 15 2. Pile installation and its effect on surrounding soil Pile installation can be modelled with the use of CEM, through the activation of a prescribed displacement. In PLAXIS this function is called prescribed line dis- placement, entailing a load that acts horizontal and/or vertical in the soil with a prescribed movement [PLAXIS, 2017b]. The prescribed line displacement can be applied on a soil cluster, a structure or by itself in/on the soil. The prescribed line displacement will occur in the direction and magnitude applied, either fixed, free or prescribed in the horizontal and/or vertical direction. When using a prescribed line displacement is a restriction that an initial cavity must be modelled with a radius over zero, even if this is not the case in reality where the expansion starts from a cavity with a radius of zero. However, should this not influence the result [Castro and Karstunen, 2010]. If only the influence on the surrounding soil is of interest the cavity can be left empty, as there is no reason to model the pile material [Castro and Karstunen, 2010]. How- ever, is the drawback that no interaction between the soil and the pile in the form of interfaces etcetera can be modelled. If the cavity instead is filled with a mate- rial acting as the pile, the interaction can be better captured. Favourable could a LE material be used as this would not collapse due to the high applied strains [Abu-Farsakh et al., 2015]. Another way to model the expansion of a soil cluster in PLAXIS is through vol- umetric expansion, which corresponds to the displaced volume of soil that occurs during the pile installation [PLAXIS, 2017b]. Through, the function volumetric strain, where a positive volumetric strain corresponds to an expansion and a neg- ative shrinkage. The software adjusts the stresses and forces that occurs in the surrounding soil. Therefore, the total volumetric strain may not be applied to the cluster. Hence, the resulting deformations is dependent on the ratio of stiffness be- tween the cluster with volumetric strain and the surrounding soil. Thus, sometimes a larger volumetric strain must be applied in order to reach a specific final expan- sion, if the clusters have different properties. The prescribed line displacement is therefore more numerically stable [Castro and Karstunen, 2010]. To simplify the modelling of mass displacement as a consequent of pile installation it can be beneficial to model a group of piles as one superpile. This simplification has proven to work well when soil movements far from the piling area is of interest [Edstam, 2011]. The use of a superpile can be executed in several ways, either a number or a single superpile can be modelled, where the superpile has the same cross sectional area as the sum of the piles it replaces. The superpile is then placed in the centre of the piling area. Another way to make a superpile is to model the whole piling area as a superpile and applying the rule of mixture on the superpile material, making a mix of the pile material and the soil which correlates to the volume ratio. The problem is that only mass displacement occurring outside of the piling area can be predicted. Both volumetric strain and prescribed line displacement can be used on the superpile to model the mass displacement. When making model calculations in two dimensions with a plane strain assumption can this be a good simplification, as the distance between the piles in the z-direction cannot be modelled anyway. 16 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 3 Prediction of mass displacement due to pile installation, using PLAXIS 2D There are different ways to model pile installation in PLAXIS 2D and PLAXIS 3D, but no method is fully established or verified. Therefore, to decide the optimum way to model the consequences of pile installation, in relevance with the Thesis aim, were different approaches evaluated in PLAXIS 2D. All the models were constructed with a pre-installed pile in the soil, which then was expanded with different functions. The constructed pile was either a cavity or contained a linear elastic material. Hence, were the models based on the CEM. The influence of the disturbance from the pile installation was not investigated, e.g. the influence of the installation technique. Only the volume-change in the soil due to the pile installation. The constitutive models used were Linear-Elastic, Mohr-Coulomb, Soft Soil and Soft Soil Creep. The reason to investigate several constitutive models were that the simpler models such as LE and MC would cope with larger deformations before collapse, hence did the trials started with these before the more advanced models were used. 3.1 Investigation and chosen modelling technique To decide which model and modelling technique was best suited for the calculations in PLAXIS, in the Thesis, a number of models were carried out. Firstly, was an axisymmetric model constructed with a general soil profile and model parameters. In which three different versions to model mass displacement were carried out. The first model contained a cavity with a prescribed line displacement. The problem were either the occurrence of soil collapse or that the prescribed line displacement tugged in the nodes. Hence, not giving an accurate distribution of the mass dis- placement and deformation of the mesh. Another drawback was that no interaction between the soil and the pile could occur. Whereas, when modelling a soil cluster with a LE material an interaction could be obtained. Furthermore, did the defor- mation of the mesh occur smoother, resulting in a more plausible mass displacement. The plane strain model was, as the axisymmetric model, constructed with a gen- eral soil profile. Where, compared to the axisymmetric model, more than one pile could be modelled. Therefore, it was investigated if the influence of the pile order could be captured. This were done both with prescribed line displacement and vol- 17 3. Prediction of mass displacement due to pile installation, using PLAXIS 2D umetric strain. Firstly, three soil clusters were constructed, which the prescribed line displacement or volumetric strain were activated upon. One pile at a time was activated in three following phases, mimicking the pile order. As the piles were constructed as soil clusters the mesh was deformed when the first pile was installed, including the not yet activated piles. Hence, resulting in deformed piles before ac- tivation. To counteract this problem were different measures carried out, including embedded beam rows in the soil clusters which would not deform before activation, with varying results. Furthermore, it was investigated if the deformed piles nevertheless would cause un- symmetrical deformations and displacement of the soil; which could be linked to the pile order. A couple of additional piles were therefore constructed in the model, to give large deformations. The result showed minor unsymmetrical deformations that could be linked to the mesh as well as the pile order and the technique was ruled out. The main problem when modelling mass displacement with the function volumet- ric strain, was the uncertainty of how much the soil cluster would expand, as the applied volumetric strain can be overruled due to other parameters in the model. As the depth entails higher stresses and strains in the surrounding soil can it be assumed that the volumetric expansion will decrease with the depth if the same volumetric strain is set for the entire soil cluster. A scenario where the volumetric strain increased with depth were therefore carried out, resulting in some difference in the outcome. However, the uncertainty of the amount of volumetric strain which had been applied remained. When investigating the function prescribed line displacement, it was set to occur horizontal and uniformed. Whereas, the movement in the vertical direction were either set to free or fixed. Both with and without the use of interfaces. Thus, could the interaction between the surrounding soil and pile be somewhat captured. When not using interfaces, letting the prescribed line displacement move in the vertical direction there was a significant drag down of the pile, even when the unit weight of the pile was the same as the soil. The chosen model technique for this Thesis was to use a plane strain model, with a superpile and prescribed line displacement. A plane strain model was chosen as unsymmetrical geometries could be modelled and the scenarios investigated in the Thesis correlates well with the plane strain assumption. A superpile was chosen as the modelling of individual piles and pile order gave small to zero differences in deformation. Lastly was prescribed line displacement used as displacement is more numerical stable, in contrary to the function volumetric strain. 18 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 3. Prediction of mass displacement due to pile installation, using PLAXIS 2D 3.2 Deriving model parameters It is important to distinguish between soil properties and model parameters, as soil properties give information on how the soil reacts in different situations, depend- ing on loading/unloading and soil characteristics to name a few. Whereas model parameters are input values used in different constitutive models to capture the be- haviour of the soil. As no constitutive model fully captures the soils behaviour it is important to choose parameters that will make the model act in the way that is sought. 3.2.1 Study site The Thesis investigates the mass displacement occurring in Gothenburg and more specific in the area around the Central Station, due to the installation of precast concrete displacement piles. The area around the river Göta älv, were the Central Station is located, consist of soft sensitive clay underlying a layer of fill which was placed in the area around 200 years ago. Before this both the north and the south side of Göta älv were reed areas, see Figure 3.1. Figure 3.1: Map over the area around Gothenburg Central Station, inside the circle, in 1790, to the left and in 1890 to the right. After the fill of dredged material was placed, modified from [Ramböll AB et al., 2015]. The thickness of the clay layer is up to 100 metres on both sides of the river. On the South side is the layer of fill between three to four metres, consisting of both friction fill and dredged material [Sabattini and Wallgren, 2018]. Underlying the clay is a layer of friction material which varies from zero to two metres in thickness, before solid bedrock. The groundwater level varies in the area depending on the distance to Göta älv, as the groundwater varies with the water level in the river. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 19 3. Prediction of mass displacement due to pile installation, using PLAXIS 2D Most of the model parameters used in the calculations are retrived from investi- gations made for Regionens Hus and from the Design Base - Geoteknik made for Västlänken Station Centralen [Wood, 2017]. From here on after referred to as the Design Base in the Thesis. Parameters further come from field and laboratory tests carried out for Västlänken Station Centralen. For the clay the constitutive models SS and SSC were chosen, and for the fill and friction material was MC used. Whereas, the superpile was modelled with a LE material, so it could cope with the large strains occurring when the prescribed line displacement was activated. The material was a concrete material retrieved from PLAXIS Tutorial Manual, Tutorial 13, where the unit weight was modified to correlate with the clay, to prevent drag down [PLAXIS, 2018b]. All parameters for the fill, friction material and clay materials can be found in Appendix A, Table A.1 and Table A.2, respectively. 3.2.2 Pre-consolidation pressure The pre-consolidation pressure (σ′c) is in more advanced models a key parameter, that changes throughout the soil profile [Karstunen and Amavasai, 2017]. In the SS and SSC models is the variable especially sensitive in relation to over consol- idated ratio (OCR) and pre-overburden pressure (POP). To derive the parameter the OCR and the POP from the Design Base were used, and the vertical effective stress, instead of using e.g. the Casagrande method. σ′c was plotted against the vertical effective stress, where the difference between them is either OCR or POP, see Appendix A, Figure A.1. The values derived were used as an input parameter in the PLAXIS SoilTest for both the IL Oedometer and Triaxial compression tests, see Chapter 4.3. 3.2.3 Poisson’s ratio for loading and unloading Poisson’s ratio for loading and unloading (vur) is an elastic parameter which in PLAXIS is set to be constant, commonly assumed to range between 0.1 and 0.2 [Karstunen and Amavasai, 2017]. In the Thesis it was set to 0.15 for all clay layers. The SS models tend to not be especially sensitive to the assumed vur, but when it comes to models and predictions where the horizontal stresses are of importance it is advised to perform a sensitivity analysis of the parameter. Hence, as the Thesis investigates both the horizontal and vertical mass displacement was a sensitivity analysis performed on the vur, see Chapter 4.3. 20 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 3. Prediction of mass displacement due to pile installation, using PLAXIS 2D 3.2.4 Modified compression, swelling and creep index In the SS and SSC models are the modified parameters for compression (λ∗) and swelling (κ∗) the key parameters for the soils stiffness [Karstunen and Amavasai, 2017]. In the SSC model is also the modified creep index (µ∗) a vital stiffness parameter. Both λ∗ and κ∗ can be derived from either IL Oedometer tests or CRS tests. The parameters can be derived directly from graphs by plotting the logarithmic rela- tionship between volumetric strain (εv) and mean effective stress (p′) [PLAXIS, 2017a], see Figure 3.2. Figure 3.2: Logarithmic relation between εv and p′, giving the values for λ∗ and κ∗. For the Thesis were µ∗ retrieved from the Design Base and λ∗ and κ∗ was retrieved from IL Oedometer test performed for Västlänken Station Centralen on the depths of 8, 15, 19 and 45 metres. The resulting values of λ∗ and κ∗ were plotted against the depth creating an interpolation of the values between the test depths, these graphs can be seen in Appendix A, Figure A.2 to Figure A.6. 3.3 Construction of Base Model in PLAXIS 2D A Base Model was constructed with a plane strain model, 15-nodes and SS model. The chosen soil profile can be seen in Figure 3.3, where the first layer of fill consists of friction material and begins at level +2.5 metres, in the model. The second layer of fill consists of dredged material and starts at level +1.5 metres, following are five clay layers with different sets of model parameters and lastly a layer of friction material before the bedrock. There are two different geological deposits between clay layer 3 and 4 on a depth of 20.5 metres, where the model parameters differ significantly, especially with consideration to κ∗, λ∗, OCR, effective cohesion (c′) and effective friction angle (φ′c). CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 21 3. Prediction of mass displacement due to pile installation, using PLAXIS 2D Figure 3.3: Schematic illustration over the chosen soil profile in the Base Model. The Base Model contained a horizontal ground surface, and was 200 metres wide with the superpile structured in the centre, see Figure 3.4. The superpile was con- structed as a soil cluster, on which the prescribed line displacement was added. The soil cluster had a width of one metre from the beginning. The prescribed line displacement was set to be prescribed in the horizontal direction and fixed in the vertical direction to prevent drag down. The pile was not included in the original Base Model due to how the superpile differed depending on the design of the piles. Both sides of the superpile was structured in the model, to be able to try different unsymmetrical cases. A borehole was structured in origo where the layers of fill, clay and friction material as well as the water table, was set. The water table was set to level ±0 in the model, the top of the first clay layer. The horizontal boundaries (xmin and xmax) were set to be closed for ground water flow in the clay layers, but seepage was allowed in the friction material and fill. The minimum vertical boundary (ymin), was also set to be closed for groundwater flows. Whereas the maximum vertical boundary (ymax), was set to be open. The bedrock typically consists of some crushed or cracked areas, therefore not initially closed for groundwater flow as a closed ymin entails. However, as a friction material layer which allowed for groundwater flow was placed on top of the bedrock was this argued to be a valid assumption. 22 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 3. Prediction of mass displacement due to pile installation, using PLAXIS 2D Figure 3.4: The Base Model in PLAXIS 2D. The mesh of the Base Model was constructed through applying a coarseness factor of 0.5 to the model and refining the mesh. This gave a quality of the mesh where two elements had a size under 0.5 and 13 elements under 0.6. The result was sym- metrical, without a too time consuming calculation time. Furthermore, the mesh could cope with the large strains that occurs when activating the prescribed line displacement. A finer mesh could lead to model collapse, as smaller deformations are allowed. To investigate the models capacity, if it could cope with the deformations, stresses and strains due to mass displacement, the OCR was firstly set to 10 for all clay layers. Thus, making the the model behave falsely Linear Elasto-Plastic and see if the model could handle the deformations, before using the chosen OCR values in the model for SS and SSC. 3.3.1 Calculation of prescribed line displacement The prescribed line displacement was calculated to correlate with the amount of piles installed. Where it was assumed that no volume change would occur in the soil when the piles were installed, due to the low permeability of the clay. Hence, the volume of piles installed were assumed to be the same volume as the mass displacement. The equation used considered the piling area, number of pile rows and number of piles among other things. The reason to calculate the cross sectional area, seen from above, of the piles and piling area, in contrary to the volume of the piles and piling area; were that the ratios were equal, as the depth and height of the pile and piling areas was the same. A schematic illustration of a general piling area, seen from above, can be viewed in Figure 3.5. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 23 3. Prediction of mass displacement due to pile installation, using PLAXIS 2D Figure 3.5: Schematic illustration over a general piling area, seen from above. The equation used to calculate the prescribed line displacement can be seen in Equa- tion 3.1. Prescribed line displacement = (wsp ∗ √ ( asp apa + 1) − wsp 2 (3.1) Where: wsp - width of superpile; number of pile rows ∗ pile width asp - area of superpile; (pile diameter)2 ∗ number of piles apa - piling area; wsp ∗ length of piling area The ratio between the area of the superpile to the area of the total piling area, soil included, was calculated. Hence, the percentage of piles with consideration to the total area. It was assumed that the area would increase the total percentage calculated. Furthermore, it was assumed that each pile would increase equally in all directions. As the Thesis investigates a two dimensional case, where the mass dis- placement only can occur in two directions was the percentage square rooted. Hence, the percentage each side of the pile was increased to get the total area increase. This was then multiplied with the width of the superpile, and then subtracted with the width of the superpile (the number of pile rows installed in that step) to get the total prescribed line displacement that should be applied in the model, in that step. As the prescribed line displacement were applied in two directions was the total prescribed line displacement divided by two. 24 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 3. Prediction of mass displacement due to pile installation, using PLAXIS 2D 3.3.2 Calculation phases The Base Model were calculated through a number of calculation phases, in all phases were the pore pressure set to be phreatic, suction ignored and the mesh set to be updated. Furthermore, different structures were activated and deactivated in the different calculation phases, see Table 3.1. The plastic procedures can generally be viewed as the undrained response and calculation, and the consolidation phases as the drained calculation and response. Table 3.1: Calculation phases used in the Base Model. Calculation Phase Procedure Activated structures Inital phase K0 Generates the initial stresses, the two fill layers were deactivated. No structures were activated. Phase 1 Plastic Activation of the dredged fill. Phase 2 Consolidation Consolidation for 10 years, letting the excess pore pressure from the activation of the fill dis- sipate. Phase 3 Plastic Activation of the friction fill. Phase 4 Consolidation Consolidation for 10 years, letting the excess pore pressure from the activation of the fills dis- sipate. Phase 5 Consolidation Consolidation for 178 years, until present day, letting the excess pore pressure from the acti- vation of the fills dissipate. Phase 6 Plastic No additional structures were activated, the dis- placements that had occured during the previ- ous steps were reset to zero. The nil-step fur- thermore made the stress field be in equilibrium, and made the stresses obey the failure condi- tion. Phase 7 Consolidation Consolidation for one year in order to be able to validate the excess pore pressure and settle- ments with values measured in the area. The reason to model the previous soil history, although the model parameters are derived from the current soil, was to obtain the stress and strain state in the soil. Which is a consequence of the soil history. Furthermore, is the excess pore pres- sure also created through the modelling of the soil history. Whereas, directly after the Initial Phase no excess pore pressure is existing in the model. The nil-step only resets the displacements, hence the stresses, strains and pore pressures are still there. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 25 3. Prediction of mass displacement due to pile installation, using PLAXIS 2D To validate the Base Model before calculations were carried out, the excess pore pressures during the control year in the model and the occurring settlements in the field were compared. The settlements in the area around Gothenburg Central Sta- tion is as most two millimetres per year [Wood, 2014]. The model gave a vertical settlement of approximate 1.5 millimetres. Therefore, the settlement rate was valid, as the model captured the behaviour. The excess pore pressure in the area, due to the placement of the fill, varies, see Appendix A, Figure A.7. In the Base Model the pore pressures simulated were com- pared to the ones measured in the field. The excess pore pressures occurring in the model at the control year can be viewed in Figure 3.6. When compared to the mea- surements in Appendix A, Figure A.7 can it be seen that the maximum excess pore pressure in the Base Model occurs around level -30 to -42 metres, with a magnitude of 12 kPa, which correlates fairly well to the measured excess pore pressures on that depth in the area, see Appendix A, Figure A.7. This validation could not be done for the SSC model, as the model creates large pore pressures to simulate the creep. Hence, gave exorbitant excess pore pressures in the control year. Figure 3.6: Excess pore pressures in the Base Model during the control year. 26 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 4 Validation of model and modelling technique Field measurements were derived from two construction projects to verify chosen modelling technique, the Base Model and the equation for the prescribed line dis- placement. The projects investigated where the pile installation for one of the bridge support abutments of Partihallsbron and the pile installation in section 0/550 to 0/600 of the lowering of the highway E45, which stretches from Lilla Bommen to Marieholm. From now on in the Thesis the projects are referred to as Partihallsbron and E45 respectively. The pile installation, and consequently mass displacement, for the project Partihallsbron, have been studied in technical reports such as the SBUF-reportMassundanträngning i samband med pålslagning i lera, [Edstam, 2011]. Hence, the number of piles, pile installation order and field measurements are well documented in comparison to general construction projects. The soil profile for the two projects are nearly identical, as they are located in close proximity to each other, in typical Gothenburg clay. Further is E45 located in the area from which the model parameters were derived, see Figure 1.2. 4.1 Field measurements and project information from Partihallsbron and E45 The vertical field measurements for Partihallsbron came from bellow hoses, which were placed from level ±0 to -45 metres. The horizontal field measurements came from inclinometers retrieving information between the same levels. The field mea- surements evaluated in the Thesis were derived from four locations adjacent to the piling area, see Figure 4.1. The measurements of the vertical mass displacement was derived on a distance of 12 and 20 metres from the piling areas centre, on the long side of the piling area. Hence, the distance to the superpile, the locations are marked with smooth rings in Figure 4.1. Whereas, the field measurements of the horizontal mass displacement were taken from the short side of the piling area, marked with dotted rings in Figure 4.1. Because, the location from where the vertical field mea- surements were retrieved, had faulty horizontal measurements. Thus, were instead measurements on the short side with roughly the same distance used, 14 respectively 24.5 metres. Although, from the edge of the piling area as the superpile stretches throughout it. Whilst, in PLAXIS the result is retrieved 12 and 20 metres from the superpile centre and from the long side of the piling area. Same as the result for 27 4. Validation of model and modelling technique the vertical mass displacement, due to the setup of the model. Thus, the horizontal field measurements is an approximate benchmark as the field measurements should be smaller further from the piling area, and on the short side. Figure 4.1: Schematic illustration over the piling area for Partihallsbron and the location from where the field measurements were retrieved, modified from [Edstam, 2011]. For E45 the field measurements were retrieved from Project Navet, and settlement gauge plates measuring the vertical movement of the ground surface. A total of six points were evaluated in the Thesis. The points were located 20 (D), 38 (E), 50 (F), 60 (A), 65 (B) and 74 (C) metres from the centre of the piling area, hence superpile, see Figure 4.2. The distance was measured as a straight line from the superpile, and assumed to be on the same distance horizontally in the model. One thing that differentiates the two projects with relevance to the Thesis and mod- elling, was the size of the piling area. The piling area in Partihallsbron was 16.2 metres long. Whereas, the length of the section investigated in E45 was 50 metres. Hence, the piling area for E45, better corresponds to the plane strain assumption. However, where it fewer uncertainties around the geometry and field measurements from Partihallsbron. Thus, through modelling both projects the influence of plane strain and accurate model geometry could be evaluated. 28 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 4. Validation of model and modelling technique Figure 4.2: Illustration over E45, where the dots inside the circle are installed piles. The circle marks the chosen section and the points A-F the location from where the field measurements were retrieved, modified from [Trafikverket, 2018]. The piling area for Partihallsbron were horizontal, though the information was lack- ing on which level the pile installation occurred from. Hence, if the pile installation was performed from top of fill, or if the fill were partly excavated and replaced with a piling bed, made of i.e. gravel. This information was not retrieved from E45 either, as the geometry of the area has differed during the project. Through, excavations of soil masses, placement of gravel beds, construction of slopes etcetera. Therefore, a horizontal model in PLAXIS was used. Through using field measurements from both sides of E45 the results could be better evaluated as the geometries differs. The location of Point D, E, F were closer to existing buildings and slopes. Whereas, the location of Point A, B, C were located closer to another construction project which installed piles, Regionens Hus see Figure 1.2. As no information was retrieved on if the pile installation were performed from top of fill or if the fill were partly excavated and replaced with a piling bed. Three scenarios were modelled for both Partihallsbron and E45 : • Scenario 1: The pile installation was performed from top of fill. • Scenario 2: The fill was excavated/removed and replaced with a 0.1 metre thick piling bed consisting of gravel, from where the pile installation then was performed. • Scenario 3: The fill was excavated/removed and replaced with a 0.2 metre thick piling bed consisting of gravel, from where the pile installation then was performed. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 29 4. Validation of model and modelling technique 4.2 Calculations of Partihallsbron and E45 The Base Model was used for both projects and from the nil-step were different phases added to simulate the different scenarios, parameter validation and valida- tion of prescribed line displacement. The pile installation for Partihallsbron was performed in three stages. The installed piles had a length of 52 metres and pile width of 275 millimetres. Number of piles and pile rows and the calculated prescribed line displacement can be seen in Table 4.1. The calculated prescribed line displacement from each calculation phase were added onto the previous. No information on the time span for the pile installation were available. Hence, the pile installation was simulated in three calculation phases which each lasted one day in PLAXIS, with no intermediate consolidation phase. Table 4.1: Prescribed line displacement for Partihallsbron. Phase Number of Pile rows wsp asp/apa Prescribed line piles [mm] displacement [mm] 1 9 1 0.275 0.15278 10.1303 2 22 2 0.550 0.18673 24.5769 3 29 2 0.550 0.24614 31.9845 The pile installation for E45 was performed during two weeks, week 50 and 51 year 2016. Thus, the pile installation in PLAXIS were simulated in two calculation phases, each lasting five days. Intermediate consolidation phases, lasting two days, were included after each pile installation phase; to simulated the weekend since the work was assumed to only occur on weekdays. The chosen weeks and the section were somewhat isolated from other pile installation and construction work on E45. Due to the holidays no pile installation was performed during week 52. Thereof, could one week of consolidation in PLAXIS be compared with the field measure- ments for week 52 without concern for external disturbances. The installed piles had a length of 65 metres and a pile width of 275 millimetres. Number of piles and pile rows and the calculated prescribed line displacement can be seen in Table 4.2. Where, as in Partihallsbron, the prescribed line displacement for the second calculation phase was added onto the previous. Table 4.2: Prescribed line displacement for E45. Phase Number of Pile rows wsp asp/apa Prescribed line piles [mm] displacement [mm] 1 36 3 0.275 0.06600 13.3950 2 26 3 0.550 0.04767 9.7168 30 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 4. Validation of model and modelling technique For the calculation phases for Partihallsbron see Table 4.3, and for E45 see Table 4.4. Both projects were consolidated for 80 years after the final pile installation phase with SS and SSC model, to investigate the influence of creep. This was carried out for Scenario 1. Otherwise, was the result only derived from the models using SS model. Table 4.3: The calculation phases used in Partihallsbron, Scenario 1. Phase Procedure Activated structures Phase 8 Plastic First pile installation phase. Phase 9 Plastic Second pile installation phase. Phase 10 Plastic Third pile installation phase. Phase 11 to Phase 17 Consolidation Consolidated for 10 years in each phase until 80 years was reached. Table 4.4: The calculation phases used in E45, Scenario 1. Phase Procedure Activated structures Phase 8 Plastic First pile installation phase Phase 9 Consolidation Consolidated for two days. Phase 10 Plastic Second piling phase Phase 11 Consolidation Consolidated for two days. Phase 12 Consolidation Consolidated for seven days. Phase 13 Consolidation Consolidated for seven days. Phase 14 Consolidation Consolidated for 80 years. For the calculations of Scenario 2 and Scenario 3 the material used as the piling bed was the friction material, used in the Base Model. When modelling the removal of fill were the fill layers deactivated after the nil-step and the piling bed activated. Following were consolidation phases with the purpose to dissipate most of the ex- cess pore pressures generated when the bed was placed. The calculation phases for Partihallsbron can be seen in Table 4.5, and for E45 in Figure 4.6. As before the phases do follow the nil-step. After one year of consolidation the maximum excess pore pressure was 32.16 kPa, thus within the range measured in the area, see Appendix A.1, Figure A.7. Furthermore, the model was consolidated for 1.5 and 2 years, the excess pore pressure did not decrease significantly. Thereof, was one year of consolidation considered to be sufficient. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 31 4. Validation of model and modelling technique Table 4.5: Calculation phases used in Partihallsbron, for Scenario 2 and Scenario 3. Phase Procedure Activated structures Phase 8 Plastic Deactivation of the fill layers. Phase 9 Consolidation Consolidation for one year. Phase 10 Plastic Activation of piling bed, 0.1 or 0.2 meters. Phase 11 Consolidation Consolidation for one year. Phase 12 Plastic First pile installation phase. Phase 13 Plastic Second pile installation phase. Phase 14 Plastic Third pile installation phase. Phase 15 to Phase 22 Consolidation Consolidated for 10 years in each phase until 80 years was reached. Table 4.6: Calculation phases used in E45, for Scenario 2 and Scenario 3. Phase Procedure Activated structures Phase 8 Plastic Deactivation of the fill layers. Phase 9 Consolidation Consolidation for one year. Phase 10 Plastic Activation of piling bed, 0.1 or 0.2 meters. Phase 11 Consolidation Consolidation for one year. Phase 12 Plastic First pile installation phase Phase 13 Consolidation Consolidated for two days. Phase 14 Plastic Second piling phase Phase 15 Consolidation Consolidated for two days. Phase 16 Consolidation Consolidated for seven days. Phase 17 Consolidation Consolidated for seven days. Phase 18 Consolidation Consolidated for 80 years. 4.3 Validation of model parameters and prescribed line displacement To evaluate the influence the prescribed line displacement and the model parameters κ∗, λ∗ and vur had on the resulting mass displacement, a sensitivity analysis of the parameters was performed. Through, decreasing and increasing the calculated and derived values. This was done for Partihallsbron with Scenario 1. The sensitivity analysis was further validated against field measurements. The prescribed line displacement was halved and doubled, with comparison to the original value, to determine the accuracy needed and validate the derived Equation 3.1. The result on the vertical mass displacement can be seen in Figure 4.3, along with the result for the original line displacement and field measurements. Through, halving the prescribed line displacement the result was underpredicted, and the dou- bled line displacement overpredicted the mass displacement. The same result was obtained for the horizontal mass displacement, see Appendix B, Figure B.1. 32 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-31 4. Validation of model and modelling technique Figure 4.3: Resulting vertical mass displacement for the high-, low- and original line displacement, and field measurements for Partihallsbron, Scenario 1. An overpredicted prescribed line displacement influenced the result more than an underpredicted. As the line displacement was halved or doubled can it be argued that the difference was no surprise. However, the prescribe line displacement was still relatively small as the final prescribed line displacement for the case with low line displacement were approximate 0.033 metres, the original line displacement ap- proximate 0.067 metres and the large line displacement 0.13 metres. The result shows that the calculation for the prescribed line displacement may not be accu- rate to the extent that it captures the field measurements fully; which is probably due to other factors as well, such as model parameters, the SS model which fails to capture the hardening due to small strain stiffness, certain margin of errors in the field measurements etcetera. However, the calculation gives a prescribed line displacement that captures the mass displacement adequate without modifying the prescribed line displacement after the field measurements. Whereas, a calculation that would give larger or lower values would not capture the field measurements. Hence, it can be concluded that for this model the calculation for the prescribed line displacement was verified, giving resulting mass displacement