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Title Title

Issue 41, 2017

Plaxis Bulletin

Predicting Pile Driving Induced Movement in Gothenburg Soft Clay

Back analysis of Caen’s test by the recently developed frozen/unfrozen soil

Table of contents

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Colophon

Any correspondence regarding the Plaxis Bulletin can be sent by e-mail to:

[email protected]

or by regular mail to:

Plaxis Bulletinc/o Annelies VogelezangPO Box 5722600 AN DelftThe Netherlands

The Plaxis Bulletin is a publication of Plaxis bv and is distributed worldwide among Plaxis subscribers

Editorial team:Ronald BrinkgreveErwin BeerninkMartin de KantArny LengkeekVincent KeizerJudi GodvlietJasper van der Bruggen

For information about PLAXIS software contact your local agent or Plaxis main office:

Plaxis bvP.O. Box 5722600 AN DelftThe Netherlands

[email protected]: +31 (0)15 251 7720Fax: +31 (0)15 257 3107

The Plaxis Bulletin is the combined magazine of Plaxis bv and the Plaxis users association (NL). The Bulletin focuses on the use of the finite element method in geotechnical engineering practise and includes articles on the practical application of the PLAXIS programs, case studies and backgrounds on the models implemented in PLAXIS.

The Bulletin offers a platform where users of PLAXIS can share ideas and experiences with each other. The editors welcome submission of papers for the Plaxis Bulletin that fall in any of these categories.

The manuscript should preferably be submitted in an electronic format, formatted as plain text without formatting. It should include the title of the paper, the name(s) of the authors and contact information (preferably e-mail) for the corresponding author(s). The main body of the article should be divided into appropriate sections and, if necessary, subsections. If any references are used, they should be listed at the end of the article. The author should ensure that the article is written clearly for ease of reading.

In case figures are used in the text, it should be indicated where they should be placed approxi-mately in the text. The figures themselves have to be supplied separately from the text in a vector based format (eps,ai). If photographs or ‘scanned’ figures are used the author should ensure that they have a resolution of at least 300 dpi or a minimum of 3 mega pixels. The use of colour in figures and photographs is encouraged, as the Plaxis Bulletin is printed in full-colour.

Editorial0304 New developments

Predicting Pile Driving InducedMovement in Gothenburg Soft Clay

08

PLAXIS Expert Services update06


12

Plaxis Americas20Recent activities22

www.plaxis.com l Issue 41, 2017 l Plaxis Bulletin 3

We are pleased to release the Autumn 2017 edition of the PLAXIS Bulletin, including two new user articles on PLAXIS 3D and the PLAXIS 2D Thermal with the Frozen/Unfrozen Barcelona Basic Model. We also highlight some upcoming developments and review our recent activities like our PM4Sand roadshow, new additions to the PLAXIS 2D and 3D software, as well as some new Python based tools.

In the New Development column we review the history of our Dynamic module which started in 1998 in PLAXIS 2D and was later extended with PLAXIS 3D Dynamics in 2011. The segment continues to discuss upcoming new calculation possibilities and a new material model, PM4Sand, which should all become available in 2D 2018. Through these developments we ensure that users can rely on PLAXIS to offer state of the art facilities for liquefaction and general dynamics analysis.

In the PLAXIS Expert Services update we discuss constitutive modelling services provided to Tractebel Engineering in order to model compressible elements for tunnel linings in PLAXIS 3D. The work was delivered as a User Defined Soil Model and offered the client a quick, convenient and time-saving solution for their projects.

In the first user contributed article the authors discuss the three-dimensional modelling done as

part of the development of three new buildings with basement levels, situated in a triangular site. The site will feature as a large transport hub connecting the eastern parts of Gothenburg. The three-dimensional analysis was necessary due to project requirement calling for a detailed ground movement analysis to confirm the impact of pile driving near the adjacent existing infrastructure. In the second article the authors investigate the behavior of the Caen’s silt in frost heave through physical experiments. This Caen silt is highly frost susceptible. The authors then performed a back analysis with PLAXIS 2D and the Thermal module, as well as the new Frozen/Unfrozen Barcelona Basic model, in order to prove the merit of using PLAXIS 2D to estimate potential damages due to frost heave. The Plaxis Americas segment discusses the past activities held in the western hemisphere, like courses, but more importantly, the West Coast seminars on dynamic analysis and PM4Sand. Existing users, but also people unfamiliar with PLAXIS, were invited through several seminars to find out about our user friendly and robust solutions to perform dynamic analysis and were introduced to the more increasingly used PM4Sand model soon to be available in PLAXIS 2D.

In Recent activities, we discuss the new PLAXIS Coupling Tool bringing the structural and geotechnical

engineering communities together, the PLAXIS 2D to 3D converter, and the new geotechnical capabilities introduced in the PLAXIS 2D and 3D 2017 releases.

We hope you will enjoy another solid edition of PLAXIS related content and we look forward to receive your feedback on this 41st edition of the PLAXIS Bulletin!

The Editors

Editorial

4 Plaxis Bulletin l Issue 41, 2017 l www.plaxis.com

Title Title

Ronald Brinkgreve, Plaxis bv

Since 1998, PLAXIS has dynamic modelling capabilities. In the first decade of existence, the use of the PLAXIS Dynamic Module was primarily meant to analyse wave propagation in the sub-soil that is caused by external or shallow source vibrations. Since 2008 the necessary functionality has gradually come available to enable different aspects of advanced geotechnical earthquake analysis. With the upcoming 2D 2018 version the PLAXIS Dynamic Module is fully ready for pre- and post-liquefaction analysis and geotechnical earthquake design in general.

Geotechnical earthquake analysis requires special boundary conditions, such as tied degrees-of-freedom, free-field and compliant base boundaries. Tied degrees-of-freedom are used to model one-dimensional wave propagation in a thin soil column to enable a detailed ground response analysis. Results can be presented in the time domain as well as by frequency spectra. Free field and compliant base boundaries are meant to absorb waves from the model domain propagating beyond the model boundaries, thereby modelling the proper interaction between the far field and the model domain whilst avoiding spurious reflections at the model boundaries. This enables a realistic 2D and 3D dynamic analysis of soil-structure interaction problems, including liquefaction evaluation. The latest developments involve three main new dynamic features:

• PM4Sand model: next generation constitutive model for liquefaction analysis

• Updated Mesh in dynamic calculations allowing for large deformation dynamic analysis

• Coupled dynamic-consolidation analysis: Dissipation of excess pore water pressure in dynamic calculations.

The PM4Sand model, developed by Professor Ross Boulanger and Dr. Katerina Ziotopoulou of UC Davis [1], is an advanced liquefaction model, calibrated on data from case histories and cyclic lab tests. The determination and calibration of model parameters is straight-forward; especially with the cyclic DSS test available in the PLAXIS SoilTest facility (Figure 1). This makes the model highly applicable for practical applications. With a proper calibration of model parameters, the model can accurately predict

liquefaction behaviour, and with the post-liquefaction ‘switch’ in the model, it also enables lateral spreading and other post-liquefaction phenomena. The PM4Sand model in PLAXIS has been validated against the original version 3 of the model, developed by UC Davis. Details will be presented at the GEESD V conference in Austin, Texas, in June 2018 [2].

The development of the PM4Sand model fits in the PLAXIS tradition of implementing good constitutive models for practical geotechnical applications. This tradition started with the linear elastic perfectly plastic Mohr-Coulomb model, followed by the implementation of the Hardening Soil model [3]. Regarding the latter model, we would like to commemorate professor Tom Schanz, who passed away recently. Tom devoted a significant part of his habilitation in the nineties to the development and validation of the Hardening Soil model, in collaboration with PLAXIS researchers. We would like to express our sincere condolences to his relatives and express our appreciation for the research that Tom did for PLAXIS.

Hereby I would like to conclude this column of New Developments. With the existing and new dynamic capabilities, you can rely on PLAXIS, providing state-of-the-art facilities for liquefaction analysis and geotechnical earthquake design in general. We look forward to hear about your experience with these facilities in practical applications.

Ronald Brinkgreve

References:• [1] Boulanger, RW and Ziotopoulou, K (2015).

PM4SAND (version 3): A sand plasticity model for earthquake engineering applications. Report No. UCD/CGM-15/01. Center for Geotechnical Modeling, University of California at Davis.

• [2] Vilhar G, Laera A, Foria F, Gupta A, Brinkgreve RBJ (2018). Implementation, validation and appli-cation of PM4Sand model in PLAXIS. GEESD V, Austin, Texas (to be published).

• [3] Schanz T, Vermeer PA, Bonnier PG (1999). The Hardening Soil model: Formulation and verification. Beyond 2000 in Computational Geotechnics – 10 years of PLAXIS. Balkema, Rotterdam, 281-296.

New Developments


Title Title

Figure 1. Results of undrained cyclic DSS test simulation with the PM4Sand model


Title Title

Nicolas Lambert, Senior Geotechnical Engineer at Tractebel

In the framework of PLAXIS Expert Services, Tractebel has been supported in developing a non-linear constitutive model for the 3D behaviour of compressible elements for tunnel lining.

ContextIn weak rock or under high overburden, considerable displacements occur during excavation of tunnels and galleries. The stresses developing in many cases exceed the yield limit of standard linings, frequently leading to severe damages and the necessity of costly repairs. To allow for a safe and economical tunnel construction, strategies have to be used, which guarantee support characteristics compatible with the strains, and at the same time utilize the supports as much as possible.

One system consists in loading steel tubes (arranged parallel and in layers) perpendicular to their axis, which leads to an oval shape, when loaded (see figure 1).

Modelling workWhen these elements are submitted to a compression force (see figure 2), they first behave elastically (tube stiffness – phase 1). In a second time, the tubes begin to collapse and the stiffness of the element is strongly decreased (phase 2). Beyond a certain load, the tubes are completely crushed and the stiffness of the element increases again, back to a value close to the initial one (phase 3).

The modelling strategy here consists in representing such flexible segment lining as volume element and developing a specific constitutive material law in the framework of a UDSM (User Defined Soil Model). The user defined model works on the set of following set of user-input value input value:

• E1: Elastic Young's modulus in local 1 direction• E1, plas: Equivalent elastoplastic Young's modulus

in local 1 direction during buckling• e1,b: Deformation at start of buckling• e1,e : Deformation at end of buckling• E2: Elastic Young's modulus in local 2 direction

• E3: Elastic Young's modulus in local 3 direction• G12: Shear modulus in local 12 directions• G23: Shear modulus in local 23 directions• G31: Shear modulus in local 31 directions• Local Coodinates Type: Specification of local

coordinates system: 1 is rectangular local axis 2 is cylindrical local axis

• Dir2X: Axial direction X• Dir2Y: Axial direction Y• Dir2Z: Axial direction Z• CenterX: X-coordinate of point on axis of revolution

if Local Coodinates Type=2• CenterY: Y-coordinate of point on axis of revolution

if Local Coodinates Type=2• CenterZ: Z-coordinate of point on axis of revolution

if Local Coodinates Type=2

The local axes directions are supposed to be defined as follows:

• Direction 2 is parallel to the tunnel axis;• Direction 3 is perpendicular to the tunnel lining;• Direction 1 is perpendicular to both directions

2 and 3; it is the direction in which the trilinear behaviour is available.

Input values of the model parameters E1, E2, E3, G12, G13, G23 has to be calculated by the user based on:

• Ematerial

• Tube thickness and diameter• Outer frame thickness• Inner frame thickness

PLAXIS Expert Services helps Tractebel developing a UDSMfor the behavior of compressible elements for tunnel lining in PLAXIS 3D

Figure 1. Illustration of the adjustable flexible segment lining technique


Title Title

• Tube Spacing in local 2 direction• Number of tube in local 3 direction

Once implemented the UDSM has been validated against available test data and finally used in complex 3D projects also involving tunnel intersection (see figure 3).

About TractebelAt the helm of the Energy Transition, Tractebel provides a full range of engineering and consulting services throughout the life cycle of its clients’ projects, including design and project management. As one of the world’s largest engineering consultancy companies and with more than 150 years of experience, it's our

mission to actively shape the world of tomorrow. With about 4,400 experts and offices in 33 countries, we are able to offer our customers multidisciplinary solutions in energy, water and infrastructure.

Figure 2. Typical behaviour of adjustable flexible segment liningFigure 3. 3D tunnel application

(a) Connectivity plot – (b) Major principal strains

“Use of compressible elements is a key point in the present gallery application. Such structures could not be modelled easily in PLAXIS with the existing behaviour laws. A workaround solution consisted in slicing the calculations into sub-stages with Python

scripting, but this solution was very difficult to manage for a complex 3D model. The development of a specific UDSM by PES helped us getting quickly a convenient and

time-saving solution to our problem.”

Nicolas Lambert, Senior Geotechnical Engineer at Tractebel


Neighbouring works by Trafikkontoret included new double tram tracks on two of the three sides of the property. All tram lines around the property were designed as elevated bridge structures or piled deck structures and the dual train line consists of a station on a piled bridge structure. Hence, there were substantial risks concerning ground interactions between the different piled structures for tram, train and the new development. Furthermore, the footprint of the new building was to be maximised, while simultaneously trying to minimise any interaction with the adjacent infrastructure, requiring an innovative engineering approach.

The primary geotechnical challenge for this site was predicting lateral soil displacement as a response to driving of 350 precast, reinforced concrete piles with square dimensions ranging from 235mm to 350mm. The piles needed to be driven to 40m below ground to support the new structure. Hercules Grundläggning was commissioned to carry out the piling works.

The main construction measure applied to prevent heave and lateral movements in neighbouring areas was pre-augering to a depth of 12m before installing a precast pile into the void and driven to the design depth. GDG’s responsibility was to predict the movements due to pile driving.

Yeganeh Attari, Paul Doherty, Paul Quigley - Gavin & Doherty Geosolutions, Dublin, Ireland. Nicholas Lusack - Sigma Civil AB, Stockholm, Sweden

Gavin & Doherty Geosolutions Ltd. (GDG) conducted an extensive study, analysing the effects of pile driving in extremely soft

clay for a development in Gamlestad, Gothenburg. GDG was commissioned by Sigma Civil Engineering Ltd. who were providing

design advice to Serneke Construction Ltd. The proposed development comprised of three buildings ranging between 5 to 18

stories in addition to two basement levels, planned to be built on a triangular shaped site. The development will act as a transport

hub interlinking trains, trams and buses connecting the eastern parts of Gothenburg (Figures 1 & 2). The piled site is bounded by

the Gamlestad bridge (supported on piles) to the west and the River Säveån to the south. The Partihallen viaduct is also located

to the south and the Marieholm tunnel project is to the west of the area planned for piling. One of the planning requirements

was to undertake a detailed ground movement analysis to confirm the impact of the construction on the adjacent infrastructure

that bordered the highly constrained site.


Figure 1. Architectural rendering of the proposed development, (Sigma Civil Ltd.)


Ground ConditionsThe ground conditions represent some of the most challenging soils that exist worldwide, with the soft clay extending to more than 40m depth, necessitating extensive piling works.

GDG reviewed the site-specific geotechnical information to produce a ground model that incorporated the stratigraphy and mechanical soil characteristics. The available site investigation testing identified the generalised ground conditions as comprising approximately 40m of soft ground material overlying bedrock. Material properties of the soil were estimated based on the recommendations by Edstam & Kullingsjö (2010) for Gothenburg soft clay. The undrained shear strength of the soil (cu) was deemed to be 15kN/m2 with a gradient of 1kN/m2/m and a constant average stiffness of approximately 10MPa was assumed. Furthermore, an undrained behaviour was defined for the surrounding soil to allow for the occurrence of lateral and vertical displacements generated as a result of volumetric expansion during pile installation. Methodology

The act of installing the piles would cause the site to expand laterally outwards, stressing the existing foundations of adjacent structures. GDG was tasked with accurately modelling the pile installation and quantifying the level of interaction between the new piles and the existing construction. As a result, a cost effective pile design was developed that allowed the project to economically proceed, while simultaneously minimising any negative impacts on the adjacent structures.

The numerical analysis to predict the effect of pile installation into the soft soil on the adjacent buildings was undertaken using PLAXIS 3D Finite Element (FE) package. The pile driving was simulated using the volumetric expansion method (VEM), by simulating Volumetric Strain within the soil body. This feature allows changes in an element’s volume that induces additional stresses in the surrounding soil which introduces deflections around the model until a global equilibrium of stresses is reached. A Linear Elastic constitutive model was used to model the sub-soil. This soil model was chosen since the deflections

considered were relatively large and outside the “small strain” zone. The main aim of the study was to capture the Large Strains occurring in close distances from the piles as a result of driving. Furthermore, this soil model had provided satisfactory results in previous research of Gothenburg Clay soil movements (Edstam & Kullingsjö, 2010; Nenonen & Ruul, 2011). Although the Linear Elastic constitutive model is recognised as a relatively simple soil model in comparison with non-linear models, the successful use of it in previous research on Gothenburg Clay and the subsequent calibration detailed below made it a favourable choice for the purpose of this project.

Considering the complexity of the problem and the highly non-linear nature of the calculations, it was deemed necessary to validate the approach using a simplified geometry. In other words, Careful calibration was essential in validating the Linear Elastic model so that the results could be considered accurate. Hence, the numerical problem was initially validated using a single pile expansion and comparing the numerical results to published data from related research conducted by Xu et al. (2006). In his study, Xu

Figure 2. Aerial photo of the triangular shaped piling site bounded by railway bridge, river and tram lines, (www.hitta.se)

Description Value

Soil Unit Weight (kN/m3) 17

Poisson’s Ratio, o 0.2

Young’s Modulus, E (MPa) 9.6

Table 1. Soil Parameters employed in the PLAXIS models


et al. (2006) managed to predict ground movements caused by pile installation using Shallow Strain Path Method (SSPM). This method suggests that during pile installation, movements in the surrounding soil are relative to the pile tip movement similar to the flow of an incompressible inviscid fluid around the pile tip. The output of the single-pile installation analysis in Plaxis was compared with the results generated from the empirical method recommended for this problem by Xu (2006) and good agreement was found between the results (see Figure 3).


Following validation, the numerical model was then expanded to take into account multiple pile installations according to the pile layout drawings for the site. The reaction of the buildings adjacent to the piling area was also simulated using a superpile approach. This methodology allowed groups of smaller piles supporting the structure to be represented as single ‘superpiles’ which were expanded to the equivalent volume of soil displaced by the sum of the real piles. The models took into account the effect of the pre-bore intended to be performed

during construction. For this reason, no volume expansion was assigned to the top 12m of the piles. Furthermore, the pre-existing foundations of the adjacent bridge structures were also modelled as piled rafts surrounding the new piling location, based on the as-built drawings (see Figure 4).

ResultsBased on the results of the FE analysis, the foundation of the buildings located to the south and south-west of the piling site were not excessively affected by the

Figure 3. Predicted heave generated due to a single pile driving in soil using PLAXIS compared to Xu et al. (2006) results

Figure 4. Developed numerical model in PLAXIS



pile driving. However, the results suggest that the piles to the immediate west of the foundation may be damaged due to piling works since the distance between the two sites was less than 1m. It was also observed that the new pile installations could detrimentally affect the adjacent piled structures by generating excessive moments and shear forces in the exiting piles. For these areas, the use of bored piles instead of driven piles was recommended. Further numerical predictions indicated that buildings on the west side of the piling site could be in a critical situation if pile driving was conducted closer than 7.5m to them, allowing a minimum safe piling distance to be established. The maximum displacement predicted in the soil adjacent to the piling works was predicted to be circa 50mm (as indicated by the displacement contours in Figure 5).

Construction phaseThe models were reviewed by Trafikkontoret and it was concluded that a maximum lateral displacement of approximately 50mm was to be expected for the most critical adjacent structure due to the new pile installation works. Given the innovative nature of the design, GDG recommended a practical observational approach to validate the results by using on-site

monitoring to record the ground movements. This approach also validated the accuracy of the 3D simulations. During the piling operations shown in Figure 6 inclinometers were installed on site in order to monitor the soil displacements in the area. All structures were additionally monitored by surveying structural movements in all directions. It can be concluded that the FE analysis gave very accurate result and actual maximum soil movements were recorded to be below 50mm.

The maximum movement has since decreased as the effective stress have equalised following completion of the piling works. Ultimately, the project was completed on time and in budget, largely due to the complex numerical modelling that allowed a detailed piling sequence to be developed.

Summary Points• The extensive depths of soft clay (>40m) underlying

Gothenburg pose a significant challenge for constructing deep foundations.

• Lateral displacement of soil due to pile driving is a particular concern for adjacent structures.

• Pre-boring can partially reduce the impact of pile driving.

• Detailed 3D numerical modelling using cavity expansion approaches can accurately simulate the piling induced soil displacements.

• Calibration of such numerical models is critical to determining accurate results.

• The Gamlestad project was successfully completed with no negative impact on the surrounding structures.

• The predicted movements of the soft clay were seen to accurately represent the lateral displacements observed during construction.

References• Edstam, T., & Kullingsjö, A. (2010). Ground

displacements due to pile driving in Gothenburg clay, Proc. Numerical Methods in Geotechncial Engineering, Benz & Nordal (eds), p625–630.

• Xu, X.T., Liu, H.L. and Lehane, B.M (2006). Pipe pile installation effects in soft clay, Proc. Geotechnical Engineering (October), 285–296.

• Nenonen. P & Ruul. J (2011), Environmental impact of pile driving (An FE-analysis of the displacement of the Skäran bridge), Master's Thesis, Chalmers University of Technology.

Figure 5. Results of numerical model analysis in PLAXIS

Figure 6. A view of the construction phase, (Sigma Civil Ltd.)


Frozen/unfrozen soil modelThe frozen/unfrozen soil model was recently developed by Ghoreishian Amiri et al. (2016b). The model is able to represent many of the fundamental features of the behavior of frozen soils, such as the ice segregation phenomenon and strength weakening due to pressure melting. This is a two-stress-state variables model based on the solid phase stress and cryogenic suction. The solid phase stress is defined as the combined stress of soil grains and ice, and the cryogenic suction is defined as the pressure difference

between ice and liquid water phases, which can be calculated using the Clausius-Clapeyron equation (Thomas et al., 2009):

H. Rostami, S. A. Ghoreishian Amiri , G. Grimstad - Norwegian University of Science and Technology (NTNU), Trondheim, Norway

Prediction of frost heave is crucial in the design and safety analysis of structures on frost susceptible soils. Frost heave is defined

as an upward displacement of soil caused by sucking in water during a freezing period. Frost heave is one of the major sources of

damage to transportation infrastructures, such as roads, pipelines, and railways. Caen frost heave experiments were operated in

a large-scale laboratory facility in Caen, France, by Canadian and French researchers. The incentive was to study how soil around

a chilled pipe, which carries a cold liquefied gas, will behave. In this paper, the recently developed frozen-unfrozen soil model

(Ghoreishian Amiri et al., 2016a) is applied for back analysis of the experiment. The model is available as a user defined soil model

in PLAXIS 2D. The object of this article is to show PLAXIS abilities in THM analysis of frozen soils.


r is a constant related to the maximum stiffness of the soil, b is a parameter controlling the rate of change in soil stiffness with suction and Sseg is the threshold value of suction for the ice segregation phenomenon. Figure 1 shows the complete yield surfaces of the model in p q S- -) ) space for m 0= . Figure 2 shows the influence of m on the shape of the yield surface at a constant value of .s 0 01w = .

The details of the model formulation and parameters determination can be found in Ghoreishian Amiri et al. (2016a) and Aukenthaler (2016), however, the main parts of the model are briefly reviewed here. The yield surfaces of the model are defined as:

(3)

(4)

(5)

(6)

where

and p) is the solid phase mean stress, q) denotes the solid phase deviatoric stress, M stands or the slope of the critical state line, kt is the parameter for describing the increase in apparent cohesion with suction, m is a constant controlling the shape of the yield surface with unfrozen water saturation, pc) indicates the reference stress, l denotes the

compressibility coefficient of the system within the elastic region, 0m represents the compressibility coefficient for the unfrozen state along virgin loading,

*w ws p= −σ σ I (1)

(2)0

lnw i iTS p p lT

ρ= − = −

where v) is the solid phase stress (compressive stress is negative), sw is the unfrozen water saturation (i.e. the ratio of the volume of unfrozen water on the volume of frozen and unfrozen water), pw denotes the water phase pressure (pressure is negative), I denotes the unit tensor, s is the cryogenic suction, pi denotes the ice phase pressure, it indicates the density of ice, l is the specific latent heat of fusion, T stands for temperature on the thermodynamic scale and T0 is the thawing temperature of ice.

( ) ( ) ( )2*

* * *1 0.m

t t w y tqF p k S p k S s p k SM

= − − − − + =

2 / 0.seg wF S S s= − =

[ ]0 (1 )exp( ) rr Sλ λ β= − − +

0

0

** *

*y

y cc

pp p

p

λ κλ κ−−

=

Figure 1. Three-dimensional view of the yield surfaces inp*- q* - S space for m=0

Figure 2. Influence of m on the shape of the yield surface inp* - q* plane at sw = 0.01


Hardening rules are defined as: the Caen silt was used, and for low frost susceptible soil SNEC sand was used. A steel pipeline carrying a cold liquefied gas with 5mm wall thickness, 27.3cm diameter and 210 GPa elastic modulus was buried 33cm below the surface. All lateral boundaries were thermally and hydraulically closed, the bottom boundary was adiabatic and permeable, and the top boundary was impermeable but with imposed temperature. Figure 3 shows a schematic view of the facility.

Two major cycles of freezing and thawing were conducted in this experiment, first started in September 1982 with four freezing and three thawing periods, and lasted until May 1989. A second cycle of freezing and thawing periods was run between 1990 and 1993. In this study, just one of the freezing periods from the first cycle of freezing and thawing is simulated. In this period, the top boundary had a temperature of -0.75oC and the pipeline temperature

1 1 1seg sp mpv v

seg at s s s s seg

dS e e Sd dS p S

ε ελ κ λ κ

+ += + − + + +

Where mpdε and spdε are the plastic parts of strain due to the solid phase stress and cryogenic suction variations, respectively.

Finally, the flow rules are defined as:

11 *

mp Qd dλ ∂=

∂ε

σ

22

sp Fd dS

λ∂

= −∂

ε I

where 1dλ and 2dλ are the plastic multipliers and

1Q is the plastic potential function.

2 2* **

1 2y t

w

p k S qQ s pM

γ +

= − +

Note that, there are small modifications in equations (2) and (8) compared with the original formulation introduced in Ghoreishian Amiri et al. (2016a).

Caen’s experimentThis large-scale test facility (16m long, 8m wide and 1.75m high) was constructed at Station de Gel at Le Centre de Geomorphologie at Caen, France (Dallimore, 1985). In this test, two soils with obviously different frost susceptibility were used for creating the same situation as in the field. For highly frost susceptible soil

(11)

(10)

(9)

(7)

(8)

0

0

*

*0 0 0 0

1 1y mp spv v

y

dp e ed dp

ε ελ κ λ κ+ +

= − −− −

Figure 3. Schematic view of Caen’s facility (Selvadurai et al., 1999)


was maintained at a constant value of -5oC, while the initial temperature of the system was 4oC. Deformations were measured and reported for four points (sites) on the surface of the soil body. A schematic view of monitoring locations is given in figure 4.


Model setupThe THM version of PLAXIS 2D is used for the simulation. Due to symmetry, one half of the cross section is considered. The mesh used for the simulation is shown in figure 5. The water table is located at 90 cm below the surface but the whole domain is assumed to be saturated due to capillary action. The material properties of the model are given in

tables 1-6. The “Van Genuchten” model parameters for unfrozen water content and relative permeability versus temperature are estimated based on curve fitting to experimental data (figures 6-7).

Figure 4. Schematic view for the cross section of Caen’s test (Selvadurai et al., 1999)

Figure 5. Spatial discretization of the domain



Simulation resultsThe simulation was conducted for 359 days. The contour of ice saturation after 359 days is shown in figure 8. As expected, freezing is initiated from two areas; around the pipeline and from the top boundary. As shown in the figure, frost penetration occurs slowly and there is still an unfrozen area in the domain after 359 days. As expected from the unfrozen water content curve, some unfrozen water remains in the frozen area.

Figure 6. Unfrozen water saturation versus temperature Figure 7. Relative permeability of the soil versus temperature

Figure 8. Ice-saturation contour after 359 days

Table 1. General properties of soil Table 4. Constitutive model parameters of soil Table 5. Thermal properties of water and ice phases

Table 6. Pipeline properties

Table 2. Hydraulic properties of soil

Table 3. Thermal properties of soil



The temperature contours showing the evolu-tion of the freezing front during the freezing period are presented in figure 9. Similar to ice saturation results, some portion of silt still has a temperature above the freezing temperature even at the end of the simulation. In figure 10, the simulation results for the evolution of the 0oC isotherm for the period of 50 days is compared with the experimental results (Smith and Patterson, 1989). In the figure, the simulation results for 0oC isotherm after 50 days of freezing is shown with the white line, which should be compared with

the first black line representing the experimental results of the 0oC isotherm for the same period of freezing. As shown in the figure, simulation results are in a reasonable agreement with the experiment.

Figure 11 shows the frost heave at the end of the freezing period. A total heave of 22 cm is observed around the centerline of the pipe at the end of the simulation period. In figure 12, the heave displacement at monitoring points (sites 1-4) located right above the centerline, 25 cm, 60 cm and 100 cm from the centerline of the pipe, are compared with the simula-

tion results, and reasonable agreement is achieved. The simulation results for pipe movement are also compared with the experimental results in figure 13. Frost heave occurs by transport of water into the freezing front. Figures 11-13 show that PLAXIS can successfully simulate this phenomenon, and figure 14 shows transport of water into the frozen area of the soil. This could end up in formation of ice lenses in the soil body. Note that PLAXIS uses a continuum approach for simulating the frost heave phenomenon, and cannot directly simulate ice lens forming.

Figure 9. Temperature profiles at selected time steps

Figure 10. Comparison of simulated and experimental results for the 0oC isotherm after 50 days



Figure 11. Frost heave after 359 days

Figure 12. Heave displacements from experiments and simulation



Figure 13. Pipe movement from experiment and simulation

Figure 14. Transport of water into the frozen area



ConclusionIn this article, the frozen/unfrozen soil model is used for back analysis of Caen’s frost heave experiment. The THM version of PLAXIS 2D is used as the finite element platform of the simulation. Caen’s experiment is a field-scale test reporting frost heave deformation of soils due to freezing, and has been used as a benchmark problem for validating computational models. Frost heave is a coupled THM phenomenon that occurs by transport of water into the freezing front of frost susceptible soils like silt.

Temperature distribution and frost heave deformation resulting from the simulation are compared with the experimental data at different locations in the domain, and reasonable agreement is achieved. Results show the capability of the model in simulating the frost heave phenomenon as a result of ice segregation.

AcknowledgmentThis work is carried out as part of SAMCoT (Sustainable Arctic Marine and Coastal Technology) project supported by the Research Council of Norway though the Centre for Research based Innovation.

References• Aukenthaler, M. (2016) The frozen unfrozen barcelona

basic model: A verification and validation of a new constitutive model. Msc thesis, Delft University of Technology.

• Dallimore, S. (1985) Observations and predictions of frost heave around a chilled pipeline. Msc thesis, Carleton University.

• Ghoreishian Amiri, S. A., Grimstad, G., Aukenthaler, M., Panagoulias, M., Brinkgreve, R. B. J. & Haxaire, A. (2016a) The frozen and unfrozen soil model.

• Ghoreishian Amiri, S. A., Grimstad, G., Kadivar, M. & Nordal, S. (2016b) Constitutive model for rate-independent behavior of saturated frozen soils. Canadian Geotechnical Journal 53(10):1646-1657.

• Selvadurai, A. P. S., Hu, J. & Konuk, I. (1999) Computational modelling of frost heave induced soil–pipeline interaction: II. modelling of experiments at the caen test facility. Cold Regions Science and Technology 29(3):229–257.

• Smith, M. W. & Patterson, D. E. (1989) Detailed observations on the nature of frost heaving at a field scale. Canadian Geotechnical Journal 26(2):306-312.

• Thomas, H. R., Harris, C., Cleall, P., Kern-Luetschg, M. & Li, Y. C. (2009) Modelling of cryogenic processes in permafrost and seasonally frozen soils. Géotechnique 59(3):173-184.


Plaxis Americas

The year 2017 has been a very dynamic year in many respects – we have been very active working with and for our clients, as well as giving extra attention to dynamic analysis and earthquake engineering in PLAXIS. More on the recent West Coast seminars on dynamic analysis and the PM4Sand model below.

Courses, trainings and morePlaxis Americas has continued to offer a variety of educational events, ranging from free one-hour webinars to multiday classroom courses. Classroom courses of note were the standard courses in New York in April and in Charlotte NC in December, the advanced course in New York in July and the master classes in New York and Los Angeles. The first master classes were tailored towards practitioners working on geotechnics in the urban environment industry to provide a good understanding of Plaxis 2D for earth retaining structures and deep foundations, and deep excavations respectively. Other master classes offered were dedicated to tunnel engineering and dynamic analysis.

In addition, Plaxis provided a diverse portfolio of services under the Plaxis Expert Services program such as model reviews, mentoring and tailor-made online and in-house trainings sessions in the US and Canada. Plaxis Americas engineer Sean Johnson provided several multiday in-house trainings sessions in 2017. A noteworthy training was requested by a large regional governmental agency that, although it currently does not have PLAXIS licenses, frequently is confronted by proposals using PLAXIS, and therefore feels the need to learn more about geotechnical finite element modeling in general, and PLAXIS specifi-cally. A desire was expressed to focus on giving a deeper understanding of how PLAXIS users decide on constitutive model selection and associated input date consistency, and how sensitive results are by decisions made by the PLAXIS user. A tailor-made straightforward two-day program was planned that included sessions on topics such as:

• determining input parameters from field data (eg SPT and CPT),

• PLAXIS SoilTest facility,

• boundary conditions, geometry selection and meshing,

• structural elements and soil-structure interaction,• initial stresses and adjacent buildings,• factor of safety and slope stability analysis,• sensitivity analysis and parameter variation facility.

Plaxis Americas presented itself at many industry events across the US and Canada, and we feel grateful and humbled seeing many papers using PLAXIS at 2017 editions of leading North American conferences such as Geo-Congress, Canadian Geotechnical Soci-ety, Deep Foundation Institute annual conference, United States Society on Dams, and Rapid Excavation & Tunneling Conference.

West Coast seminars on dynamic analysis and PM4SandAlthough PLAXIS is widely used for dynamic analysis in North America, when speaking with engineers who are not very familiar with PLAXIS, we frequently encounter misconceptions or dated information about PLAXIS’ capabilities of modeling seismic events. We believe these engineers are missing out as PLAXIS has made great progress regarding dynamic analysis and earthquake engineering in the past decade. We are convinced PLAXIS has surpassed other programs in this field, especially considering PLAXIS’ advantages regarding automatic sub-stepping, fast calculation times, and user-friendly environment.

To inform the industry, we decided to put together seminars – targeting both PLAXIS users and non-users alike – on the current state of dynamic analysis and the recent implementation of the PM4Sand model in PLAXIS 2D in the four most relevant North American regions: Vancouver, Seattle, San Francisco and Los Angeles areas. In the Seattle and Los Angeles areas we partnered with the respective local Geo-Institute chapters, and we provided two hands-on exercises giving attendees a real-life experience using the PM4Sand model in PLAXIS. Well over one hundred people attended the four seminars.

Dr. Ronald Brinkgreve, manager of the Compe-tence Centre Geo-Engineering at Plaxis, gave

an overview of the current state of modeling dynamic events in PLAXIS. His topics included:

• constitutive models such as the Hardening Soil, Hardening Soil with small strain stiffness (HSsmall), Generalized Hardening Soil (GHS) models,

• liquefaction analysis using UBC3D-PLM model (3D implementation of UBC Sand),

• material and Rayleigh damping, • input motions,• mesh considerations for a dynamic analysis,• boundary conditions (none, viscous, free-field,

compliant base, tied degrees of freedom and all node fixities),

• calculation parameters such as time steps and sub steps,

• Newmark time integration,• mass matrix,• automated pre-calculation checks,• options to display seismic calculation results.

Attention was also given to available validation studies, manuals and best-practices (available through our online Knowledge Base), as well as to the many peer-reviewed papers using PLAXIS for dynamic analysis.

Next, Dr. Ronald Brinkgreve presented on the recent implementation of the sand plasticity model PM4Sand (version 3, 2015) in PLAXIS 2D. The PM4Sand model is a stress-ratio controlled, critical state compatible, bounding surface plasticity model for sand, and was developed for geotechnical earthquake engineering applications by Professors Boulanger and Ziotopoulou at the University of California, Davis. In recent years, this constitutive model has gained significant popular-ity and now for the first time sees implementation in a widely used finite element program. Presentation topics included the main characteristics of this model, and modeling considerations for using this model in PLAXIS 2D such as the primary and secondary input parameters for this model.

At select seminars, attendees could gain hands-on experience with the PM4Sand model in PLAXIS 2D by means of two exercises. The aim of the first exercise is to simulate published CSR-N curves using


speed of these calculations, and the in-sight it gives on the PM4Sand model.

To summarize, these seminars showed attendees the current state of dynamic and liquefaction analysis using the PM4Sand model in PLAXIS. Many attendees left convinced that PLAXIS is the preferred program for

cyclic direct simple shear simulations in the PLAXIS SoilTest facility, and validates the implementation of the PM4Sand model in PLAXIS. The aim of the second exercise is to perform a 1D wave propaga-tion analysis to predict the onset of liquefaction in a sandy layer using the PM4Sand model in PLAXIS. Attendees were very enthusiastic about the ease and

dynamic and liquefaction analysis over other available programs that are either limited in scope, or more time consuming and research oriented. PLAXIS offers a well-validated, robust, and user-friendly alternative for dynamic modeling and earthquake engineering.

Plaxis West Coast seminars, left to right, top to bottom: Seattle, Vancouver, San Francisco, Los Angeles


Recent activities

PLAXIS Coupling toolWith the PLAXIS Coupling Tool, released in 2017, we bring structural and geotechnical engineers closer together, allowing users to perform advanced non-linear soil-structure interaction calculations with SAP2000 and PLAXIS 3D. Through the Coupling Tool users can select load cases from SAP and have the loads at the bottom of the SAP model transferred directly onto the subsurface model in PLAXIS 3D. In the coupling process, the calculated displacements in PLAXIS are sent to SAP in the form of updated spring stiffnesses, after which SAP recalculates the resulting displacements and forces in the structural model. The process is repeated until a balance is found.

The coupling tool also illustrates the power of the Python-based scripting environment in PLAXIS and what potential applications can be created in the framework of PLAXIS Customization Services.

PLAXIS 2D to 3D ConverterWith the PLAXIS 2D to 3D Converter, your 2D model geometry and soil properties will be converted as an extruded model in PLAXIS 3D. This eliminates cumbersome redefinition of the soil layering and material models, so users can immediately proceed with defining the remainder of the 3D model and the construction stages. Release of PLAXIS 2D 2017With the release of PLAXIS 2D 2017 we have added some geotechnical and usability improvements.

64-bit release & performance improvements PLAXIS 2D 2017 is the first full 64-bit 2D release including numerous speed improvements allowing the software to deal with more complex projects.

Cross & parallel permeability in interfacesIn the Interfaces tab of the material dataset users can now select between permeable, impermeable and semi-permeable options to define cross permeability. Parallel permeability is defined here as well. Output facilities have been extended with options to inspect the flow through and along the interfaces.

Non-linear geogridsTwo new types of behavior for geogrids are introduced. Users can now include elastoplastic, or viscoelastic behavior. For elastoplastic behavior users can define N-epsilon diagrams. With the viscoelastic behavior, creep can be taken into account for geogrids.

Python integration in Expert Menu (VIP)Using remote scripting has become more user friendly and easier with incorporation of a Python sub menu in the Expert Menu. Users can launch a Python interpreter, a Python Editor, and a Python Command prompt directly from PLAXIS to start modelling by use of the scripting language. There is

also an option to bookmark scripts and directly run favorite scripts from PLAXIS. The integration also means nice libraries can be added, one of these is the PyQtGraph packages a convenient library to use for advanced plotting options with Python.

Multiply command for numeric propertiesThe multiply command can be used to for instance multiply a set of loads with various load components by a factor higher or lower than 1. This command can be issued in the various modes on numerous objects, and especially for staged construction it offers a convenient way to explore alternate load conditions, thermal conditions, initial conditions etc.

PLAXIS Coupling tool


circular structures or parts thereof like LNG tanks, or dome shape objects, natively in PLAXIS 3D. Combining this with the existing combine, intersect and extrude tools, users can create complex shapes in their models.

Hoek-Brown parameter guideVia the side-panel of the Hoek-Brown material model users can find an interactive parameter guide for the model, consisting for example of selectable rock types and proposed magnitudes for the UCS, a searchable and clickable rock database for Mi, etc. An analysis tab is available as well, automatically plotting the major and minor principal stress based on the given parameters.

Create tunnel subsection from pointIn the tunnel designer it has become easier to create subsections, as users can define a subsection by right-clicking on a point and start the subsection from there. This speeds up drawing of, for example, an elephant’s foot or sidewall drift on your tunnel cross-section.

Release of PLAXIS 3D 2017The release of PLAXIS 3D 2017 has brought several great improvements for geotechnical modelling. Some features had previously been released in 2D 2017, which are nonlinear geogrids. Cross & parallel permeability in interfaces, the multiply command and can be read about in the PLAXIS 2D 2017 section.

Other new features include:

Elastoplasticity for plates and beamsThe material models for beams and plates have been extended with an option for elastoplasticity. Users can input yield stress and moment of resistance, and in the side panel, cross-sectional properties, plastic moment and axial force can be viewed, calculated from the input parameters. Output has been updated with tools to inspect if and where plasticity in the structural elements occurred.

Export PLAXIS model to CADVia the user interface, users can now export their whole PLAXIS model to CAD format. This can also be done through the command line where additional conditions can be given, exporting only parts of the model. The exported model can be used for post-processing or incorporation into BIM workflow. With command based *.STL generation PLAXIS models are suitable for 3D printing.

Improved sequence definition for NATM tunnels Users can now select between “TBM” and “NATM” excavation methods. The “NATM” method introduces new behaviour for the automatic generation of the construction stages. Users can define a number of slices after which the tunnel face propagation will be halted. In subsequent phases those slices will first be fully excavated before the tunnel face propagates again. This behaviour is more in line with NATM excavations in practice.

Revolve around axis toolUsers can use the Revolve around axis tool to easily create a revolving extrusion along an arbitrary axis and number of degrees to create volumes, shells or surfaces. This offers a powerful tool for modelling

Dynamically loaded rigid bodiesUsers can now apply dynamic loading to rigid bodies allowing them to model for example cyclic loads due to wind or wave loading on wind turbine foundations, or any other type of foundation which may be modelled as a rigid body.

Nurbssurface generation from point cloudThis experimental feature in the form of a command, allows users to directly import text based point cloud data into PLAXIS. Users can input the number of grid cells in two directions, which will influence the degree of approximation of the point cloud. The denser the grid the better the interpolation and approximation. Feedback from users on this feature will serve as input for future improvement and deployment of a user friendly solution for importing and processing point cloud data.

More information on how to access this feature can be requested via [email protected].

Generated NURB surface2D to 3D

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www.plaxis.com/jobsFore more information about our vacancies please take a look at our website

27 NovemberWorkshop: Practical use of PLAXIS 2D for Tunnel Applications in Geo-EngineeringInnsbruck, Austria

27 NovemberHong Kong PLAXIS Users’ Meeting 2017Hong Kong

28 - 29 NovemberWorkshop: Introduction toGeotechnical Modelling with PLAXISHong Kong

30 NovemberWorkshop: Advanced Workshop on Modelling Embankments on SoftgroundHong Kong

5 DecemberPLAXIS Online TrainingPractical use of consolidation analysisand the Soft Soil Creep model in PLAXIS

6 - 8 DecemberSTUVA Conference 2017Stuttgart, Germany

7 DecemberWorkshop on Material Modelsand Parameters in PLAXISDelft, The Netherlands

8 DecemberWorkshop on Deep Excavation in ClayShort term vs long term behaviourDelft, The Netherlands

12 - 14 DecemberAdvanced Course on Computational GeotechnicsBandung, Indonesia

12 - 15 DecemberStandard Course on Computational GeotechnicsCharlotte, NC, USA

22 - 25 January Standard Course onComputational GeotechnicsSchiphol, The Netherlands

19 - 21 FebruaryStandard Course on Computational GeotechnicsOstfildern, Germany

5 MarchIFCEE 2018Orlando, FL, USA

19 - 22 MarchAdvanced Course on Computational GeotechnicsSchiphol, The Netherlands

11 - 12 AprilWorkshop on PLAXIS for Excavation and Tunnel analysisIstanbul, Turkey

10 - 13 JuneGEESD VAustin, TX, USA

18 - 21 JuneStandard Course on Computational GeotechnicsManchester, United Kingdom

25 - 27 JuneNUMGE 2018Porto, Portugal

2 - 5 JulyICOLD 2018Vienna, Austria

Upcoming events 2017 - 2018

VACANCIESTECHNICAL WRITER (GEO-ENGINEERING)

SENIOR SCIENTIFIC SOFTWARE ENGINEERRESEARCH ENGINEER ROCK MECHANICS AND CONSTITUTIVE MODELLING

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