Numerical Analysis of a PVD-improved 

Embankment on soft clay 
Class A and class C prediction of the Ballina test 

embankments 
Master’s Thesis in Master Programme Infrastructure and Environmental Engineering 

 

SALOMON SUNDSTRÖM 

 

DEPARTMENT OF ARCHITECTURE AND CIVIL ENGINEERING 

DIVISION OF GEOLOGY AND GEOTECHNICS 

CHALMERS UNIVERSITY OF TECHNOLOGY 

Gothenburg, Sweden 2023 

  



 

 

 

I 

 

 
REPORT NO. xxxx/xxxx 

 

 

 

 

 

 

Numerical Analysis of a PVD-improved Embankment on soft clay 

Class A and class C prediction of the Ballina test embankments 

 

SALOMON SUNDSTRÖM 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Department of Architecture and Civil Engineering 

CHALMERS UNIVERSITY OF TECHNOLOGY 

Gothenburg, Sweden 2023 



II 

  



 

 

 

III 

 

 

 

 

 

 

 

 

 

Numerical Analysis of a PVD-improved Embankment on soft soil 

Class A and class C prediction of the Ballina test embankments 

SALOMON SUNDSTRÖM 

 

© SALOMON SUNDSTRÖM, 2023. 

 

Technical report no xxxx:xx  

Department of Architecture and Civil Engineering 

Chalmers University of Technology  

SE-412 96 Göteborg  

Sweden  

Telephone + 46 (0)31-772 1000 

 

 

 

 

 

 

 

 

 

Cover: excess pore pressures beneath the embankment when simulating for 1100 days. 

Gothenburg, Sweden 2023  



IV 

Numerical Analysis of a PVD-improved Embankment on soft clay 

Class A and class C prediction of the Ballina test embankments 

SALOMON SUNDSTRÖM 

Department of Architecture and Civil Engineering 

Chalmers University of Technology 

Abstract 

The construction of embankments on soft soil is challenging to engineers due to 

difficulties associated with their short and long-term stability. This thesis aims to 

utilize numerical modelling to analyse the behaviour of embankments on soft clay, 

with special focus on the Ballina test embankments. Two distinct predictions are made: 

one considering the presence of prefabricated vertical drains (PVDs) installed in the 

soil and another completely without PVDs. The constitutive model used is the Creep-

SCLAY1S model in PLAXIS 2D. The obtained results are compared with on-site 

measurements to evaluate the effectiveness and reliability of the modelling approach. 

The thesis involves analysing available soil data and creating a representative soil 

profile, deriving input parameters for the constitutive model. Furthermore, a simple 

homogenisation technique is implemented to model the global effect of the PVDs, 

through changing the vertical hydraulic conductivity in the soil. A comprehensive 

sensitivity analysis is conducted to identify factors with a significant influence on the 

simulation results. The results for the PVD-improved embankment demonstrate 

satisfactory predictions with vertical and horizontal deformations aligning reasonably 

well when compared with measurement data over a 3-year period. Moreover, the 

implemented averaging technique effectively captures the enhanced consolidation 

settlements introduced by the PVDs over the time period. Comparisons with the 

unimproved embankment indicate little actual improvements in stability for the 

improved case in the first 3 years. However, spanning over a 40-year period, the 

vertical settlements approach the same order of magnitude for the two cases, and the 

horizontal displacements are significantly less for the improved embankment. 

Indicating a time-dependent nature of stability improvement using PVDs.  

Ultimately, the parameter derivation process and high-quality laboratory data are vital 

for accurate simulations. As revealed by the sensitivity analysis, there is significant 

variations in the results depending on which laboratory test is used to derive the pre-

consolidation pressure. The discrepancy can likely be attributed to the unusually high 

strain-rates used for the CRS laboratory tests, in combination with the unusually low 

strain rates adopted for the IL-tests – emphasizing the experience and skill required of 

the engineer in order to arrive at accurate predictions.  

Keywords: Numerical modelling, creep, soft clay, test embankment, Creep-

SCLAY1S, Vertical Drains, Prefabricated Vertical Drains, PVD 



 

 

 

V 

   



VI 

Acknowledgements  

I would like to thank my supervisor/examiner Minna Karstunen for introducing me to 

the subject, for excellent guidance and for many interesting thoughts and discussions 

throughout. I would also like to thank Sinem Bozkurt for invaluable assistance with 

the numerical modelling process.  

 

Salomon Sundström 

 Gothenburg, June 2023 

 

 

  



 

 

 

VII 

 

  



VIII 

Table of contents 

1. Introduction ........................................................................................................ 1 

1.1. Aim and Objectives ....................................................................................... 1 

1.2. Limitations .................................................................................................... 2 

2. Background ......................................................................................................... 3 

2.1. Behaviour of Soft Soil ................................................................................... 3 

2.1.1. Consolidation and creep ......................................................................... 4 

2.1.2. In-situ stresses ........................................................................................ 9 

2.1.3. Yielding and rate dependency .............................................................. 11 

2.1.4. Sample disturbance .............................................................................. 13 

2.2. Embankments on Soft Soil .......................................................................... 15 

2.3. Prefabricated Vertical Drains ...................................................................... 18 

2.4. Plane Strain and PVD Performance ............................................................ 24 

2.5. Numerical Modelling of Soft Soil ............................................................... 26 

2.6. Creep-SCLAY1S Model ............................................................................. 28 

2.6.1. Parameters ............................................................................................ 33 

3. Ballina Trial Embankments ............................................................................ 39 

3.1. Geological Setting ....................................................................................... 40 

3.2. Embankment with PVDs ............................................................................. 41 

3.3. Soil Profile .................................................................................................. 43 

4. Modelling of Embankment .............................................................................. 46 

4.1. Parameter Determination ............................................................................ 46 

4.1.1. Hydraulic properties ............................................................................ 50 

4.1.2. Parameter calibration ........................................................................... 52 

4.2. Numerical Model ........................................................................................ 54 

5. Results ................................................................................................................ 56 

5.1. Vertical Displacement ................................................................................. 56 

5.2. Horizontal Displacements ........................................................................... 58 

5.3. Pore Pressures ............................................................................................. 59 

5.4. Embankment without PVDs ........................................................................ 60 

5.5. Sensitivity Analysis ..................................................................................... 62 

5.5.1. Sensitivity of POP and OCR ................................................................ 62 

5.5.2. Sensitivity of stiffness parameters ....................................................... 63 



 

 

 

IX 

5.5.3. Sensitivity of lateral earth pressure ...................................................... 64 

5.5.4. Switching off anisotropy ...................................................................... 65 

5.5.5. Sensitivity of permeability ................................................................... 67 

5.5.6. Sensitivity of absolute rate of destructuration ..................................... 68 

5.5.7. Sensitivity of modified intrinsic creep index ....................................... 69 

6. Discussion .......................................................................................................... 70 

7. Conclusions ....................................................................................................... 73 

8. Recommendations for further research ......................................................... 74 

References ................................................................................................................. 75 

Appendix A: Embankment construction sequence............................................... 79 

Appendix B: Model input parameters ................................................................... 80 

Appendix C: Sensitivity analysis ............................................................................ 81 

  



X 

 

  



 

 

 

XI 

List of Figures  

Figure 2.1 The transformation from excess pore pressure to effective stress in soil. .. 4 

Figure 2.2. (a) Distinction between “Delayed” and “instant” and “primary” and 
“secondary” compression behaviour of soil under surcharge loading 
(Bjerrum, 1967) and (b) secondary compression and its effects on pre-
consolidation stress and void ratio in soft clay according to Bjerrum 
(1967). ...................................................................................................... 6 

Figure 2.3. Illustration of secondary consolidation (creep) and various associated 
parameters in an IL laboratory test (Olsson, 2010). ................................. 7 

Figure 2.4 Time resistance during a single weighted load step in a 1D Oedometer test 
(Svanö, et al., 1991). ................................................................................ 8 

Figure 2.5. Distribution of �′� plotted vs depth using OCR (left) and POP (right). . 10 

Figure 2.6. Evaluation of s’c from a CRS test using the Sällfors (1975) method 

(Olsson, 2013) ........................................................................................ 11 

Figure 2.7. One-dimensional CRS and IL tests by Claesson (2003) (top) and Sällfors 
(1975) (bottom) conducted using different strain rates. ......................... 12 

Figure 2.8. Soil sample quality assessment by using volumetric strain, together with 
the water content of the soil, as by (Larsson, et al., 2007). .................... 15 

Figure 2.9. Different construction methods, ground improvements and 
reinforcements utilized for constructing embankments on soft soil 
(Almeida & Marques, 2013) .................................................................. 16 

Figure 2.10. Development of settlements under surcharge loading with and without 
the use of vertical drains. (Almeida & Marques, 2013) ......................... 18 

Figure 2.11. (a) Schematic figure of an embankment on PVDs (and equilibrium 
berms) (b) detail of mandrel and footing adopted for installation and 
anchoring of the PVD (c) detail of driving mandrel and tube for 
anchoring (Almeida & Marques, 2013) ................................................. 19 

Figure 2.12. Vertical drain unit cell with surrounding smear zone (Hansbo, 1981). 20 

Figure 2.13. Influence of constant Cd on degree of consolidation (Chai, et al., 2001).
 ................................................................................................................ 22 

Figure 2.14. Different drainage conditions of PVD-improved soil (Chai, et al., 2001).
 ................................................................................................................ 23 

Figure 2.15. Direction of flow for PVDs in (a) axisymmetric conditions (b) plane 
strain conditions (Almeida & Marques, 2013)....................................... 24 

Figure 2.16. (a) Axisymmetric and (b) plane strain view of a PVD unit cell (Chai, et 
al., 1995). ............................................................................................... 25 

Figure 2.17. Typical loading paths associated with construction projects in urban 
areas (Karstunen, 2021). ........................................................................ 26 

Figure 2.18. Various classifications of elasto-plastic models (Karstunen & Amavasai, 
2017). ..................................................................................................... 27 

Figure 2.19. General stress space of Creep-SCLAY1S model (Karstunen, et al., 
2013) ...................................................................................................... 29 

Figure 2.20. Constitutive yield surfaces for the Creep-SCLAY1S model (Tornborg, 
et al., 2021). ........................................................................................... 29 

Figure 2.21 Lode angle dependency of the stress state in Creep-SCLAY1S model in �-plane (Sivasithamparam, et al., 2015). ............................................... 31 

Figure 2.22. Illustration of determination of stiffness parameters (a) � ∗, �� ∗, 	 ∗and 
(b) 
� and 
� (Gras, et al., 2017). ......................................................... 34 



XII 

Figure 2.23. Relationship between intact and reconstituted soil samples of sensitive 
clay (Yin & Karstunen, 2011) ................................................................ 37 

Figure 2.24. Procedure for determination of �� ∗ at high stress levels where all soil 
structure is erased. .................................................................................. 38 

Figure 3.1. Plan view of the Ballina National Field-Testing Facility including 
location of in-situ tests conducted at the site (Kelly, et al., 2017). ........ 39 

Figure 3.2. Geological setting of the Ballina National Field-Testing Facility (NFT) 
(Pineda, et al., 2019). ............................................................................. 40 

Figure 3.3. Illustration of the Ballina trial embankment, approximate soil profile and 
most relevant instrumentation in cross section 2 (not to scale). ............ 41 

Figure 3.4. Plan view of instrumentation at the PVD-improved embankment in 
Ballina (Kelly, et al., 2017). ................................................................... 42 

Figure 3.5. Soil properties at the site for the Ballina trial embankment .................... 43 

Figure 3.6. Example of layering procedure using CRS tests. .................................... 44 

Figure 3.7. Illustration of soft Ballina clay layer with assigned soil properties for 
each layer respectively. .......................................................................... 45 

Figure 4.1. Methodology of parameter derivation. .................................................... 46 

Figure 4.2. OCR and POP plotted vs depth using pre-consolidation pressure from 
CRS and IL-tests. ................................................................................... 47 

Figure 4.3. Derived values of � ∗, �� ∗ and 	 ∗ and �� ∗ plotted against depth. ........ 48 

Figure 4.4. Critical state line in triaxial compression from boreholes INCLO2. ...... 49 

Figure 4.5. Critical state line in triaxial compression and extension from borehole 
MEX9. .................................................................................................... 49 

Figure 4.6. Soil sample quality of conducted CRS, IL and triaxial tests from borehole 
INCLO2 and MEX9 classified according to method by Lunne et al. 
(1997). .................................................................................................... 50 

Figure 4.7. Hydraulic properties of soft Ballina clay. ............................................... 51 

Figure 4.8. Calibrated (a) CRS oedometer test at 4.89m depth and (b) IL oedometer 
test at 2.81 m depth using Soil Test Tool in PLAXIS. .......................... 52 

Figure 4.9. Calibrated triaxial (a) compression test at 9.49 m depth (b) extension test 
at 7.93 m depth. ...................................................................................... 53 

Figure 4.10. Finite element mesh of the modelled embankment. .............................. 54 

Figure 5.1. Time settlement curve for settlement plates SP1-4 compared to 
simulation results using Creep-SCLAY1S model. ................................ 56 

Figure 5.2. Time settlement curve for magnetic extensometers M0-M4 in MEX1 
borehole compared to simulation results using Creep-SCLAY1S model.
 ................................................................................................................ 57 

Figure 5.3. Settlement profile in HPG1 instrument for different time periods 
compared to simulation results using Creep-SCLAY1S model. ........... 57 

Figure 5.4. Horizontal displacements vs depth for INCLO2 instrument and Creep-
SCLAY1S instrument after (a) 60 days (b) 140 days (c) 700 days (d) 
1100 days. .............................................................................................. 58 

Figure 5.5. Time vs total pore pressure curves for VWP instruments 6a, 6b and 6c 
compared to simulation results using Creep-SCLAY1S model. ........... 59 

Figure 5.6. Time settlement curves for the case with and without PVDs for a time 
period of (a) 1100 days (b) 40 years. ..................................................... 60 

Figure 5.7. Comparison of horizontal displacements for case with and without PVDs 
after (a) 60 days, 240 days, 700 days, and 1100 days (b) 40 years. ....... 61 



 

 

 

XIII 

Figure 5.8. Time vs total pore pressure curves for simulation of embankment without 
PVDs, compared to the improved case and instruments VWP6a, b and c.
 ................................................................................................................ 62 

Figure 5.9. Influence of Pre-Overburden Pressure (POP) on vertical settlements over 
1100 days. .............................................................................................. 62 

Figure 5.10. Influence of stiffness parameter 	 ∗ (a) and �� ∗ (b) on vertical 
settlements over 1100 days. ................................................................... 63 

Figure 5.11. Influence of anisotropy parameters coefficient of lateral earth pressure 
at rest, in-situ �0 and �0�
, on vertical displacements over 1100 days.
 ................................................................................................................ 64 

Figure 5.12. Influence of coefficients of lateral earth pressure at rest, in-situ �0 and �0�
, on horizontal displacements over time periods of (a) 60 days (b) 
240 days (c) 700 days (d) 1100 days...................................................... 65 

Figure 5.13. Influence on vertical displacements when simulating with Creep-
SCLAY1S model as isotropic and with fixed anisotropy. ..................... 66 

Figure 5.14. Horizontal displacements when simulating with Creep-SCLAY1S 
model as isotropic and with fixed anisotropy. ....................................... 67 

Figure 5.15. Influence on vertical displacements by adjusting (a) horizontal and 
vertical permeability (b) overall smear effect of PVDs. ........................ 68 

Figure 5.16. Influence of absolute rate of structural degradation, ��, on vertical 
settlements over 1100. ........................................................................... 68 

Figure 5.17. Influence of the modified intrinsic creep index, �� ∗, on vertical 
settlements over 3000 days. ................................................................... 69 

 

  



XIV 

 

 



 

 

 

  1 

1. Introduction 

Soft soils, commonly found in coastal regions, often including densely populated urban 

areas, present notable challenges to the construction industry due to their unique hydro-

mechanical properties.  The stability and safety of buildings and infrastructure in these 

areas are often compromised, and the costs of construction must be balanced against high 

maintenance costs (Graham, 2006). Thus, accurately predicting the behaviour of soft soils 

over both the long term and short term is crucial for engineers when designing effective 

foundations and support systems in these complex conditions.  

In addition to engineering considerations, it is important to acknowledge the significant 

potential environmental impact of accurate predictions of soil behaviour during design 

projects. Allowing engineers to make well informed decisions of the optimal foundations 

design, thus preventing overdesign, and reducing unnecessary material usage, and will 

reduce the carbon footprint of the project and its environmental impact. Furthermore, by 

proactively addressing concerns regarding settlements, long-term stability of the 

structures is ensured, and unnecessary repairs, reconstructions, and replacements can be 

avoided with obvious environmental implications.  

Especially accurate predictions of vertical displacement at multiple depths below the 

structure, the dissipation of pore pressures and the horizontal displacements at the toe of 

the structure remain significant challenges (Amavasai et al., 2017). In present times, 

numerical modelling has emerged as a widely recognized tool for predicting soil 

behaviour under varying boundary conditions and loading circumstances. Furthermore, 

to ensure the effectiveness and accuracy of constitutive models developed for numerical 

modelling, the use of trial embankments to calibrate the models against real-world 

measurements is crucial.  

1.1. Aim and Objectives 

The aim of this master’s thesis is to utilize numerical analysis as a tool to model the 

behaviour of embankments constructed on soft soil, with special focus on the Ballina trial 

embankment located in New South Wales, Australia. The prediction will be carried out 

using the Creep-SCLAY1S constitutive model within PLAXIS 2D. The analysis aims to 

make two distinct predictions: one considering the installation of prefabricated drains 

(PVDs) at the site, and one without PVDs. The obtained results are compared with on-

site measurement data, enabling conclusions to be drawn regarding the effectiveness and 

reliability of the modelling process.  

 

 



2                      

The following objectives are set:  

• Analyse available soil data and create a soil profile representative of on-site 

conditions. 

• Derive necessary input parameters for the Creep-SCLAY1S constitutive model. 

• Perform a comprehensive numerical analysis of the Ballina trial embankment 

using the Creep-SCLAY1S model in PLAXIS 2D. 

• Model Prefabricated Vertical Drains (PVDs) using a simple homogenisation 

method for modifying the vertical hydraulic properties of the soil. 

• Conduct a class A prediction on vertical and horizontal settlements and their 

time-dependency, as well as pore pressure developments for the embankment 

without PVDs. 

• Conduct a class C prediction on vertical and horizontal settlements and their 

time-dependency, as well as pore pressure developments for the embankment 

with PVDs. 

• Conduct a sensitivity analysis on sensitive parameters and factors with high 

relevance on the prediction and draw conclusions from the results. 

1.2. Limitations  

Naturally, attempting to model the real-life behaviour of soft soil is a difficult task and 

many factors can influence the results. For this thesis, the main limitations that were 

identified are:  

• Embankment may not be sufficiently long for plane strain assumption. 

• Installation effects on the hydraulic conductivity in the soil are largely unknown. 

• Modelling PVDs in plain strain may not fully represent real-world behaviour. 

• Available laboratory tests may not be conducted at high enough stress levels to 
represent the intrinsic behaviour of the soil. 

• Measurement results for the embankment without PVDs installed were not 

available. 

• Limitations connected to the constitutive model used:  
- The elastic behaviour in the elastic region is assumed to be isotropic. 

- No small strain stiffness is included. 

- Non-linear variation of OCR is not included in the Creep-SCLAY1S 

model. 

 



 

 

 

  3 

2. Background 

The following chapter includes the theoretical background part of the conducted literature 

study. Here, the behaviour of soft soil and its key characteristic is described, followed by 

an outline of construction of embankments on soft soil, and using prefabricated vertical 

drains (PVDs) as a ground improvement method. Finally, numerical modelling of soft 

soil in general, followed by a detailed description of the Creep-SCLAY1S model and its 

input parameters is found.   

2.1. Behaviour of Soft Soil 

Deposits of soft clay have often been formed and then aged for hundreds to thousands of 

years. These deposits have been subjected to various complicated naturogenic effects, 

such as chemical bonding, surface erosion, creep, desiccation, and leaching (Bjerrum, 

1967). The process of a clay forming in-situ is referred to as “geological stress history” 

which has a significant impact on the behaviour of soil under stress (Hanzawa, 1989). 

Moreover, the magnitude of deformations depends on other factors as water content, 

density, grain-size distribution, and organic content (Larsson, 2008).   

In soil that are coarse grained the intrinsic particles are generally bound by contact with 

each other to form a skeletal cellular framework. This means a significant portion of the 

soil’s mass is occupied by pore fluids, usually water and air (Larsson, 2008). When 

subjected to deformation, soil experiences substantial and often irreversible changes in 

volume as particles rearrange. Thus, any attempt to describe soil response to loading must 

incorporate the potential for significant changes in volume (Muir Wood, 1990). This is 

especially true for deposits of soft clays where particles are sedimented slowly and in an 

undisturbed environment. Such deposits possess an open structure with large voids bound 

together by inter-particle forces rather than direct contact (fabric and bonding). As a 

result, these soils exhibit high compressibility and are prone to significant deformations 

under lading (Larsson, 2008). However, when subjected to large enough stress levels, the 

structure of soil obtained during sedimentation is erased, resulting in a shift in its 

response. Burland (1990) introduced a new concept, i.e. intrinsic properties of natural 

sedimentary clays. The intrinsic properties are inherent to the soil, meaning they are 

independent on the natural state of the soil, influenced by the soil structure and provide a 

reference when assessing the in-situ state of the soil.  

When observing soil behaviour under loading in 1D conditions it is also apparent that an 

increase in effective stress makes the soil compress (Muir Wood, 1990). A soil subjected 

to lading is experiencing compression and has the volume of its particle structure 

changed, and the pore fluids must flow throughout the soil (Larsson, 2008). Therefore, 

when applying a load to a soil specimen that is saturated, the compression is not instant. 

This is due to the soil constituents, the skeletal framework as well as the pore water being 



4                      

next to incompressible in comparison to structure of the soil (Olsson, 2010).  The only 

way for deformation to take place is by slowly squeezing water from the voids in the soil, 

see Figure 2.1. 

 

Figure 2.1 The transformation from excess pore pressure to effective stress in soil. 

For soft soil, the permeability parameter k is used to measure the extent to which the fluid 

can flow through the soil. The surface area to volume ratio increases as particle dimension 

of the soil decrease, hence a soil of small particles is most likely to be of low permeability 

and vice versa (Olsson, 2010). Water within the soil’s pores will naturally move from 

areas with higher excess pore pressures to areas where the excess pore pressures are 

lower. As illustrated in Figure 2.1, the dissipation of pore pressures will cause shift in the 

soils effective stress, leading to gradual deformation over time. This process of volume 

reduction by dissipation of excess pore pressures due to flow is referred to as 

consolidation, which will be described in more detail in section 2.1.1. 

2.1.1. Consolidation and creep 

The classic consolidation theory was developed and published by Terzaghi (1923). His 

theory is still what makes out the foundation of 1D consolidation theory today. The theory 

is developed from the assumption of a relationship between strain and effective stress that 

is not time dependent.  

Other assumptions that validate the theory are:  

• Homogenous and fully saturated soil. 

• Incompressibility of both soil particle and water. 

• Darcy’s law is applied.  

• During the consolidation process the hydraulic conductivity is a constant 

parameter. 

• Compression and pore pressure developments are in 1D. 

• Equal change in pore pressures and effective stress. 

• Strain of the soil is only dependent on changes in effective stresses, no secondary 

consolidation or creep is considered. 



 

 

 

  5 

Furthermore, the equation for Terzaghi’s one dimensional consolidation can be expressed 

through:  

���� = ��� ∙ ��� � ∙ ����! (2.1) 

where  u = pore pressure [kPa]  

M = oedometer modulus [kPa] 

t = time [s] 

γw = unit weight of water [kg/m³] 

k = permeability [m/s] 

z = depth [m] 

Assuming permeability of the soil does not vary with depth:  

���� = �" #�$���$ % (2.2) 

where cv is the coefficient of consolidation, defined as: 

c'  =  M ∙ kγ+    (2.3) 

Initially, Terzaghi’s theory was used for calculating settlements, and the consideration of 

potential settlements relating to creep began only after all excessive pore pressured had 

dissipated. Later, Taylor (1942) developed a model applicable for oedometer tests of 

effective stress vs a general variation of void ratio, e, and time, t.  

The process of consolidation has universally been divided into two distinct behaviours of 

primary consolidation and secondary consolidation. Primary consolidation refers to when 

there is an increase in effective stress and simultaneously a decrease in soil volume and 

pore pressures. On the contrary, secondary consolidation is defined as the process during 

which the soil volume decreases under constant effective stress. For many years, the 

development of creep strains in soil were considered as separate from the primary 

consolidation, and, subsequently, being equal to secondary consolidation.  

The first person that suggested clay behaves according to a relation between void ratio, 

effective stress and strain rate during one-dimensional compression was Suklje (1957). 

Suklje presented a model where creep strain was assumed to occur continuously 

throughout the consolidation process. Therefore, the model assumes that creep and 

primary consolidation are not two separate processes differentiated by the dissipation of 

excess pore pressures. Thus, Suklje demonstrated that the thickness of the clay layer, the 

permeability and the drainage conditions all have an influence on the time-dependent 

strains in the soils (Claesson, 2003; Suklje, 1957).  



6                      

About a decade later Bjerrum (1967) presented a similar conceptual model, which also 

assumes creep strains and primary consolidation are not separated processes. The 

objective of the model was to explain the relationship between geological ageing and the 

over-consolidations ratio (pre-consolidation pressure) of soft virgin clays. The model 

provides an explanation and reason for the occurrence of creep effects and settlements 

over time, despite the pre-consolidation pressure of the soil not being exceeded (Olsson, 

2010). Bjerrum stated that strains that occurred should be separated into two distinct 

components of “delayed” and “instant” compression. Figure 2.2a illustrates how clay 

compresses over time if the applied loading is instantly supported by the framework 

structure of the clay in the form of effective stress, and, consequently, causing a reduced 

void ratio in the soil. This process develops until a point of equilibrium is reached where 

the soil structure supports the overburden pressure fully and is referred to as “instant” 

compression. In Figure 2.2a, the dashed line represents the drained behaviour, where 

compression occurs without the pore water being able to delay it. The gradual rise of 

effective stresses is attributed to the viscous effect of water, which occurs as excess pore 

pressures dissipate, and compression follows along the solid line (Bjerrum, 1967). The 

concept denoted “delayed” compression is a representation of additional volume 

reduction, i.e., consolidation, taking place while the effective stress (loading) remains 

constant over time. This causes the soil sate to transition from point A to point B in Figure 

2.2b. 

 

(a) (b) 
Figure 2.2. (a) Distinction between “Delayed” and “instant” and “primary” and “secondary” compression 

behaviour of soil under surcharge loading (Claesson, 2003; Bjerrum, 1967) and (b) secondary compression 

and its effects on pre-consolidation stress and void ratio in soft clay (Claesson, 2003; Bjerrum, 1967). 

These effects are also prevalent in natural soil deposits. This can be observed in Figure 

2.2 where the soil reaches an apparent state similar to that of point B, 3000 years after the 

initial sedimentation. Within laboratory settings, i.e., 1D oedometer tests, this type of soil 

exhibits minimal strains until the stress state is equal to the pre-consolidation pressure at 



 

 

 

  7 

point C. Thus, this is where yielding is indicated in the soil, and the trajectory of the curve 

approaches the initial line representing “instant” compression (Olsson, 2010). The 

yielding of soil will be further described in section 2.1.3. 

Secondary consolidation can normally be characterized by the inclination of the e-t curve 

in an Incremental load, IL oedometer test, where the excess pore pressures in the soil have 

dissipated, see Figure 2.3 (Olsson, 2010). In order to characterize and quantify creep 

effects present in the soil, there are multiple commonly used parameters available (Cα, αs 

and rs.), with each essentially describing the same thing and is obtained through similar 

means.  

 

Figure 2.3. Illustration of secondary consolidation (creep) and various associated parameters in an IL 

laboratory test (Olsson, 2010). 

Buisman (1936) first presented a parameter describing creep behaviour defined as the 

secondary creep index Cα, which can be described using the variation in void ratio ∆e or 

the variation in strain ∆ε:   


,- = ./.012(�)  15 
,- = .6.012(�) (2.4) 

In Sweden the coefficient of secondary consolidation αs is more commonly used, which 

in turn relates to secondary compression index (Olsson, 2010). The difference is αs being 

described as a function of strain, ε, and Cα  as a function of void ration, e. The relation 

between the parameters is expressed as:  

78 = 
,1 + 6; (2.5) 

Where 1 + e0 = the specific volume, V 

 eo = initial void ratio  

The concept of time resistance, R, was developed and presented by Janbu (1969). He 

claimed it to be a powerful tool to describe time- and stress-dependent behaviour of soft 



8                      

soil under effects of compression, swelling and recompression. Figure 2.4 describes a 

single load step during a Oedometer laboratory test. The pore pressure is measured at the 

impermeable bottom of the sample while the top is drained (Claesson, 2003). Considering 

time as an action, while the strain as a reaction during creep, the time resistance, R, is 

then defined by Janbu as expressed in equation (2.6).  

< = =�=/ (2.6) 

 

Figure 2.4 Time resistance during a single weighted load step in a 1D Oedometer test (Svanö, et al., 1991). 

In Figure 2.4 the time resistance seems to be increasing linearly after a certain time t0, 

corresponding to the point when all excess pore pressures in the soil have dissipated 

(Claesson, 2003). Therefore, the gradient of this relationship, and thus the time resistance 

rs can be expressed as: 

< = 58(� − �?) (2.7) 

Where t is time and tr is the reference time.  

Due to the linear relationship of time resistance an integration from t0 to t gives a 

logarithmic creep strain with time, as seen in equation (2.8). 

/@  =  A /B
BC

=� =  A =�<  =  158
B

BC
 A  =�(� − 5?)

B
BC

= 158  0D E � − �?�; − �?F (2.8) 

 

  



 

 

 

  9 

2.1.2. In-situ stresses 

The total vertical stress at a certain level in natural soil σv is composed by the overburden 

pressure from the overlying soil masses. The vertical effective stress σ’0 is reduced by the 

pore pressures u0 present in the voids of the soil. Their relationship is expressed by: 

�′; = �; − �; (2.9) 

The pore pressure in soils can be hydrostatic from a free water table, but it can also have 

a downward gradient or an upward gradient (artesian) depending on the site conditions 

(Larsson, et al., 2007).  

If a natural soil deposit is currently experiencing the exact amount that is expected from 

the current pressure exerted by its overburden, and it has never been overloaded, it is 

normally consolidated. If a soil is unloaded after having consolidated under a certain 

effective surcharge load, i.e., the pre-consolidation pressure, σ’c, the vertical stress 

decreases, leading to the soil becoming over consolidated. The degree of over 

consolidation, OCR, is expressed as: 

G
< = �′@�′; (2.10) 

If OCR ≤ the soil is in a normally consolidated state, and when OCR>1 it is in an over 

consolidated state.  

The relationship between σ’c and σ’0 can also be expressed by pre overburden pressure 

(POP):  

HGH = �′@ − �′; (2.11) 

As evident in the general formulation of OCR and POP, they represent the distribution of �′@ due to the historical effective stress exerted on the soil in different ways when plotted 

against depth (see Figure 2.5). Therefore, considerations should be taken to which is more 

characteristic to the in situ soil conditions. Moreover, the effects of over consolidation 

can also occur due to drying or ground water fluctuations at the top of the soil profile, 

weathering effects and creep (Larsson, et al., 2007). The process of defining the pre-

consolidation pressure will be described in more detail in the next section. 



10                      

 

 Figure 2.5. Distribution of �′@ plotted vs depth using OCR (left) and POP (right). 

Deformations of fine-grained soils are due to both changes in volume and shape and 

because of its anisotropic properties it varies in different directions (Olsson, 2010). The 

relationship between the effective horizontal and vertical stresses is expressed by the 

coefficient of lateral earth pressure at rest K0: 

�; = �′I�′"  (2.12) 

For a horizontal ground surface and normally consolidated soil, the vertical stress is equal 

to the maximum principal stress, and the horizontal stress, σh, is equal to the minimum 

principal stress (Larsson, et al., 2007). The relationship between the vertical and 

horizontal effective stresses in normally consolidated soil can be uniquely expressed by 

the coefficient of earth pressure at rest in the normally consolidated region, K0
NC. It 

depends on angle of internal friction in the soil and can be automatically evaluated by 

equation (2.13). As the response of the soil depends on the anthropological and geological 

history, soils are usually not entirely normally consolidated and exhibit some apparent 

over-consolidation from historical loading/unloading as well as previously described 

creep effects (Olsson, 2013). In an over consolidated state, the value of lateral earth 

pressure at rest, �; , can be calculated by incorporating the overconsolidation ratio, OCR, 

into (2.13), through the relationship expressed in (2.14) 

�;JK = 1 − ��D LM@ (Jaky’s formula) (2.13) 

�; = (1 − ��D LM@)XYZ [\] (2.14) 

where φ’c is the friction angle at critical state.  

  



 

 

 

  11 

2.1.3. Yielding and rate dependency 

The one-dimensional consolidation of soil is an important problem to study and solve for 

the geotechnical engineer. There is no universal definition of how to define soil yielding 

(Olsson, 2013). However, the yield stress is usually evaluated from the region where the 

curve gets steeper in a compression curve plotted in a linear or log scale of stress vs linear 

strain, see dotted region in Figure 2.6. 

Various one-dimensional consolidation test configurations are employed to assess soil 

deformation and flow properties. The incremental loading test involves a cylindrical test 

specimen, that is laterally constrained by a rigid ring, and subjected to incremental 

vertical axial loading or unloading (Larsson, 2008). The constant rate of strain test (CRS) 

on the other hand, is not performed as a series of discrete stages, but a continuous process 

(Muir Wood, 2016). The upper surface of a cylindrical sample, like the incremental 

loading test, is loaded at a displacement rate (strain) that is constant over the duration of 

the test (Stolle & Stolle, 2011). Using these tests, it is possible to determine the pre-

consolidation pressure, �′@, which is often considered to be the yielding point of soft soil. 

Moreover, additional parameters relating to compression and swelling required for 

calculations and modelling can be determined.  

 

Figure 2.6. Evaluation of s’c from a CRS test using the Sällfors (1975) method (Olsson, 2013) 

The value of the pre-consolidation pressure can be derived from a laboratory test and is 

exceptionally site dependent as it is influenced by anthropological and geological 

processes. In Sweden it is common practice to define the �′@ from a standard CRS test 

using a methodology suggested by Sällfors (1975). The method is illustrated in Figure 

2.6 where the correction for strain rate is incorporated through constructing an isosceles 

triangle that determines the obtained value. This correction is done in addition to the 

recommended rate of 0.0024 mm/min adopted when conducting the test. 

It is considered a common opinion that soft soils are highly rate dependent (Olsson, 2010). 

Time dependent, long-term deformations in soil, like the previously described creep 



12                      

effect, must be considered during the design phase to avoid future problems in 

serviceability and stability (Leoni, et al., 2008). Just as in real-world conditions, strain 

rate effects are also prevalent and visible in the laboratory as well as in field testing 

(Claesson, 2003). Considering the rate of deformations in soil is crucial for interpreting 

test results and accurately predicting soil behaviour in the short term, as well as the long 

term.  

It is generally believed that when conducting a one-dimensional laboratory test, the higher 

the adopted rate of strain, the higher the pre-consolidation pressure (Olsson, 2010). This 

effect is especially evident in the normally consolidated region and can be observed in 

Figure 2.7, showing CRS and incremental loading tests conducted by Sällfors (1975) and 

Claesson (2003). 

 

 

Figure 2.7. One-dimensional CRS and IL tests by Claesson (2003) (top) and Sällfors (1975) (bottom) 

conducted using different strain rates.   

Moreover, the pre-consolidation pressure, σ’c, is often a crucial input parameter when 

modelling the behaviour of soft soil (Karstunen & Amavasai, 2017). As previously stated, 

the value of the pre-consolidation pressure can be influenced by the rate of strain of the 

conducted test. Thus, especially, when using derived parameters for modelling creep 

behaviour of soil this has large implications, as expressed by Karstunen & Amavasai 

(2017). As different clays have different tendencies to express creep behaviour (especially 



 

 

 

  13 

clays with big variations in sensitivity and mineralogy) a universal method for correcting 

values of σ’c derived from CRS tests is not possible. The method like the one described 

by Sällfors (1975) can be useful and work well for clay extracted from the same 

corresponding depths and location that was used in his work but is not accurate and 

applicable in all cases of soft soil. In later years it has been highlighted by Muir Wood 

(2016) that for more advanced non-linear, elasto-plastic modelling the interpreted results 

of laboratory CRS tests need to be used at system level (Karstunen & Amavasai, 2017).   

2.1.4. Sample disturbance 

Soil characterisation through field and laboratory testing is conducted to obtain 

information about soil properties and behaviour and is essential for the geotechnical 

design process. Field tests provide information about in-situ conditions, while laboratory 

tests determine the physical and mechanical properties of soil. Thus, obtaining reliable 

test data is paramount to making accurate predictions of soil behaviour. This is 

particularly relevant when making long-term predictions of deformation in rate dependent 

sensitive soil (Karlsson, et al., 2016). If the material properties of the investigated soil are 

not clearly identified there is little to no point in doing refined analysis. Moreover, the 

cost of laboratory testing is something that must be recovered during the design phase in 

terms of increased design confidence, savings, or improved performance (Graham, 2006). 

The disturbance of soil samples often takes place during the initial sampling process. 

According to Amundsen (2017) the main contributor to disturbance is the type of sampler 

used. The disturbance is minimal for large diameter samples, such as 160-250mm block 

samples, but it may be critical for small diameter tube and piston samples. In addition to 

the sampling process itself, it is important to acknowledge the potential impact of 

secondary disturbance on extracted soil samples. Factors such as temperature, humidity, 

transportation, and time stored can influence the clay structure and subsequently affect 

the outcomes of the tests (Amundsen et al., 2017).  

The disturbance of soil samples has a notable impact on important design parameters. 

Disturbance generally leads to a decrease in pre-consolidation pressure and the (initial) 

stiffness, while causing an increase in the stiffness post yielding (Larsson, 2008). To 

assess the quality of obtained soil samples, and therefore the influence of sample 

disturbance, there are several methods available. 

Karlsrud and Hernández-Martinez (2013) introduced the method of assessing sample 

quality by the oedometer stiffness ratio. The ratio is a comparison between the maximum 

constrained modulus (M0) within the OC stress range and the minimum constrained 

modulus (ML) obtained in the NC range. When the soil undergoes disturbance, reloading 

it into in-situ stresses results in a significant volumetric change. Therefore, a higher ratio 

of M0/ML would indicate a better soil sample quality, and vice versa. The criteria for 



14                      

which to determine the soil sample quality using the oedometer stiffness ratio is presented 

in Table 2.1. 

Table 2.1. Soil sample quality assessment criteria according to the oedometer stiffness ratio. 

Ratio M0/ML Soil sample quality 

>2 Very good to excellent 

1.5 - 2 Good to fair 

1 – 1.5 Poor 

<1 Very poor 

Lunne et al. (1997) proposed a method of evaluating the sample quality using the void 

ratio of the soil. This approach involves normalising the change in void ratio, Δ6/6;, 

which represents the amount of recompression required to restore the specimen to its in-

situ, �′";, stress conditions. The sample quality is determined using the criteria in Table 

2.2. 

Table 2.2. Soil sample quality assessment criteria using void ratio (Lunne et al., 1997). 

Δ6/6; Soil sample quality 

< 0.04 Very good to excellent 
0.04 – 0.07 Good 
0.07 – 0.14 Poor 

> 0.14  Very poor 

Andresen & Kolstad (1979) introduced the Specimen Quality Designation, SQD, which 

involves assessing the volumetric strain of a soil sample using multiple laboratory tests. 

In oedometer as well as triaxial compression tests, the volumetric (recompression) strain 

for the sample to reach the assumed in-situ vertical and horizontal effective stress is 

evaluated. The measured values are compared against the criteria presented in Table 2.3 

to assess the quality.  

Table 2.3. Soil sample quality assessment according to the Specimen Quality Designation (SQD) 

(Andresen & Kolstad, 1979). 

Volumetric strain (%) Soil sample quality 

< 1 Very good 

1 – 2 Good 

2 – 4 Fair 

4 – 10 Poor 

> 10 Very poor 

Another method for assessing soil sample quality by measuring the recompression strain 

to in-situ vertical effective stress is the one presented by Larsson et al. (2007). The method 

is grounded in the work by Lunne et al. (1997), but instead of void ratio, uses volumetric 



 

 

 

  15 

strain in combination with the initial water content, wN, to assess the soil sample quality. 

The classification criteria used for the method is presented in Figure 2.8 

 

Figure 2.8. Soil sample quality assessment by using volumetric strain, together with the water content of 

the soil, as by (Larsson, et al., 2007). 

2.2. Embankments on Soft Soil 

Constructing an embankment on soft soil if often challenging due to the compressibility, 

low hydraulic conductivity, and low undrained shear strength of the underlying soil 

deposit. The inherent properties of the soil can cause stability and settlement issues in 

both the short and long term. Consequently, careful consideration must be given to 

address these concerns during the design process. Understanding soil behaviour and 

fundamental principles of primary and secondary consolidation is essential for competent 

serviceability limit state (SLS) design (Almeida & Marques, 2013).  

When constructing an embankment on very soft soil it is anticipated that most of the 

settlements will occur after construction, as the excess pore pressures dissipate. However, 

it is crucial to give special consideration to time-dependent creep behaviour as well. By 

implementing an appropriate SLS design long-term maintenance costs of the construction 

can be avoided (Krenn, 2008). Furthermore, implications of creep is often just considered 

in relation to SLS design. Although, it may also affect the ultimate limit state design 

(ULS) of an embankment. In the case of a gradual accumulation of excess pore pressures 

due to ongoing creep under embankment loading, the mean effective stress will decrease 

as the pore pressures increase. This process can occur until the effective stress approaches 

the undrained shear strength in the soil (Krenn, 2008). Thus, the shear forces that 

previously offered resistance no longer provide any support and potentially leading to 

failure along a slip surface.  

Achieving the required factor of safety (FoS) for stability or limiting settlements to an 

acceptable degree becomes challenging, various ground improvement or reinforcement 

methods can be employed. By effectively implementing such techniques, engineers can 

mitigate the challenges associated with soft soil and ensure the long-term stability and 



16                      

performance of embankment structures. Almeida & Marques (2013) highlights a number 

of factors that should be considered when selecting the appropriate construction method 

for a specific project. These include the geotechnical properties of the soil, intended use 

of the area, construction deadlines and cost considerations. Figure 2.9 illustrates different 

construction methods, ground improvement and reinforcement techniques utilized when 

constructing embankments on soft soil. These address aspects such as settlement and 

stability control, with many approaches addressing both aspects simultaneously. In cases 

when the soil is exceptionally soft, it is common to incorporate geosynthetic 

reinforcement in combination with the alternatives in Figure 2.9. 

 

Figure 2.9. Different construction methods, ground improvements and reinforcements utilized for 

constructing embankments on soft soil (Almeida & Marques, 2013) 

According to Almeida & Marques (2013), an embankment constructed without 

employing any specific measures to mitigate settlement or stability control is referred to 

as a conventional embankment. A conventional embankment can be constructed by 

utilizing a temporary surcharge (see Figure 2.9m) with the purpose of accelerating the 

primary settlements induced and counteract all or some of the secondary settlements in 

the soil. One disadvantage of this method is the considerably large amount of earthworks 

required. Moreover, if the soil deposit is not very thick, removal of the soil may be a 

viable option (i, j in Figure 2.9), especially if the excavated material can be reused during 

the project and transport distances are manageable. However, in urban areas, finding 

suitable locations for the disposal of excavated material, can be challenging due to 

environmental concerns and possible contamination.  

Using lightweight materials, such as expanded polystyrene (EPS), is an effective 

approach to mitigate settlements induced by embankment loading (Almeida & Marques, 

2013). This technique, known as lightweight fill (Figure 2.9e), involves replacing the 

original fill material with one with significantly lower unit weight, allowing for a fast 

construction process. The lightweight fill materials, however, come at a cost.  



 

 

 

  17 

Furthermore, a reduction of embankment height (Figure 2.9d) can be considered if the 

undrained shear strength, �` , is very low in the top layers of the deposit. Although, 

depending on the project, this may not be possible due to geometry requirements of the 

road or railway. Hence, if the height of the embankment cannot be altered, and the 

projected safety factor against failure is low, it may be an alternative to construct the 

embankment in stages (Figure 2.9c), allowing an incremental increase of stability 

(Almeida & Marques, 2013). Another useful technique that can be implemented if 

stability problems are prevalent and the FoS need to be increased, is equilibrium berms 

(Figure 2.9b). However, using berms will increase the settlements, and, particularly in 

densely populated areas, space constraint may restrict potential use.  

Furthermore, constructing embankments on vertical drains can be used as a ground 

improvement method where challenges related to settlements are prevalent, especially 

when combined with temporary surcharge loading. The technique is further explored in 

this thesis and a comprehensive description will be provided in the following section.  

Embankments that are constructed on pile-like elements (Figure 2.9f, g, h) work by 

transferring the load of the embankment to a stronger soil layer or bedrock beneath the 

soft soil deposit (Almeida & Marques, 2013). This is achieved through using a platform 

with caps, geogrid, or slabs that distribute the load from the embankment to the piles or 

columns. One notable advantage of this approach is that it helps to shorten the 

construction schedule due to relatively fast installation procure. However, solutions with 

pile-like elements often come with high embodied CO₂-eq emissions. 

Specifically in Scandinavian countries, deep mixing is a widely used method for 

improving the strength and deformation properties of soft soil. This technique involves 

the creation of columns or small wall panels by blending a binding material, such as 

cement, lime, or gypsum, into the soil to achieve stabilisation (Krenn, 2008). However, it 

is important to carefully consider the environmental implications associated with the 

method when considering the design. 

Evidently, different solutions have clear perks and disadvantages associated. When 

discussing solutions such as the aforementioned conventional embankment types (Figure 

2.9a, b, c, d, m), or embankments with vertical drain-improvements (Figure 2.9k, l), an 

important aspect to consider is the time consuming nature of most of these solutions 

(Almeida & Marques, 2013). Hence, they may not be suitable if time limitations are strict. 

In such cases, solutions using pile-like elements (see Figure 2.9 f, g, h) may be preferred 

options. However, it is important to note that the latter may come at a higher monetary 

and environmental cost.  

Ultimately, the geometry of the embankment and the geotechnical characteristics of the 

site are highly variable factors that need to be carefully analysed on a case-by-case basis. 

Each project requires a thorough assessment on the specific conditions to determine the 

most suitable design.  



18                      

2.3. Prefabricated Vertical Drains 

Construction of an embankment using temporary surcharge loading is a widely adopted 

approach for addressing challenges associated with slow, long-term consolidation in soft 

soils. However, the implementation of this procedure on its own does, in practice, often 

present a challenge due to its time-consuming nature — something that is rarely an 

abundant commodity in modern design projects.  

The shortened drainage path introduced by the installation of PVDs will considerably 

reduce the consolidation time when applying a load to the soil. Thus, preloading, in 

combination with the installation of prefabricated vertical drains (PVDs), has been widely 

used by engineers as an effective ground improvement method to accelerate the 

consolidation process of soft soils under surcharge loading. The significant accelerating 

impact of vertical drains on the consolidation process of soft soil can be seen in Figure 

2.10 using an illustration of the settlement developments against time, with and without 

vertical drains installed. Moreover, by removing the surcharge after the preloading 

period, the creep settlements can also be reduced.  

 
Figure 2.10. Development of settlements under surcharge loading with and without the use of vertical 

drains. (Almeida & Marques, 2013) 

The first vertical drains adopted were sand drains in the early 1900s, which were 

subsequently replaced by PVDs (Almeida & Marques, 2013). PVDs are made of 

corrugated plastic drainage cores that make up geosynthetic elements (see Figure 2.11). 

These are installed in the soil to effectively provide decreased horizontal drainage paths 

in natural soil deposits (Rowe & Taechakumthorn, 2008). Therefore, designs that 

consider both radial and vertical drainage are often complicated. The solutions used in 

practice are usually those that ignore the effects of vertical drainage, such as the analytical 

1D unit cell solutions of Barron (1948) or Hansbo (1981). Barron (1948) presented a 

solution that incorporated, and was fundamentally built on, the legitimacy of Darcy’s law. 

The theory included two alternatives, with one assuming free vertical strains and the other 

assuming equal vertical strains, together with the combined effect of vertical and radial 

flow towards the drains. However, today, most designs today are based on the subsequent, 

simpler, and more practical, additions made by Hansbo (Müller, 2010; Hansbo, 1981). 



 

 

 

  19 

 

Figure 2.11. (a) Schematic figure of an embankment on PVDs (and equilibrium berms) (b) detail of mandrel 

and footing adopted for installation and anchoring of the PVD (c) detail of driving mandrel and tube for 

anchoring (Almeida & Marques, 2013) 

Hansbo (1981) elaborated on the principles of Barron (1948) regarding the analysis of 

enhanced consolidation in soil improved by vertical drains. His method based on equal 

vertical strain assumption and included a zone of smear and reduced well resistance. 

Other important assumptions in his theory are drainage in the soil is entirely restricted to 

the horizontal direction, the soil is totally uniform and homogenous and has constant 

compressibility and permeability.  

In practical use, the discharge capacity of a drain is naturally limited. Therefore, physical 

aspects like well resistance will have a delaying effect on the consolidation process of the 

soil, leading to degree of consolidation, expressed in (2.15), often being overestimated. 

Although, when using modern types of band-drains, the well resistance effect can 

generally be disregarded entirely in the design, due to their high enough discharge 

capacity (Hansbo, 1997). This can be seen in equation (2.17) where a simplified version 

of Hansbo’s (1981) original expression for resistance effects in the vertical drains, µ, is 

expressed, where the well resistance is ignored. Moreover, as this type of drains are 

pushed, driven, or vibrated into the soil by means of a mandrel, the effect of smear 

introduced during installation must also be considered (Hansbo, 1981).  However, it is 

challenging to estimate the extent of the disturbance caused by this. Different contractors 

utilize different techniques and equipment (penetration velocity, mandrel size and shape) 

and there are multiple ways of conducting the design process (Amavasai, et al., 2018). 

An illustration of a PVD installed in the soil, and the surrounding smear zone can be seen 

in Figure 2.12. 



20                      

 

Figure 2.12. Vertical drain unit cell with surrounding smear zone (Hansbo, 1981). 

Hansbo (1981) accounted for the smear effect by introducing a zone around the drain with 

lower hydraulic conductivity (see Figure 2.12). Assuming that Darcy’s law is valid, the 

average degree of consolidation due to radial drainage can be expressed as:  

 a? = 1 − exp �− 8� ∙ fI! (2.15) 

where the time factor Th is defined as:  

 fI = �I ∙ �gh$  (2.16) 

where  ch = coefficient of consolidation in the horizontal direction [m²/year] 

 De = diameter of unit cell [m] 

 t = time [year] 

and the value of � can be expressed as: 

where  kh = horizontal hydraulic conductivity [m/day] 

 kv = vertical hydraulic conductivity [m/day] 

 ks = horizontal hydraulic conductivity in smear zone [m/day] 

 dw = diameter of drain [m]  

 ds = diameter of smear zone [m]  

n = De/dw  

 s = ds/dw 

� = 0D D� +  I 8  0D(�) − 34 + � 20$ I3l�  (2.17) 



 

 

 

  21 

In more recent years, Basu et al. (2010) revealed that the rate of consolidation is 

influenced by both the extent of soil disturbance near the drain and the variability of 

hydraulic conductivity withing the disturbed zone. Therefore, accurately predicting the 

rate of consolidation requires identifying the hydraulic conductivity profile surrounding 

the drain.  

As soil is rarely homogenous and often has multiple layers with varying properties and 

drain installation causes disturbance in the soil, it is not always justifiable to consider 

PVD-improved soil to be under 1D conditions (Chai, et al., 1995). Hence, as the analytical 

unit cell theory, (2.15) - (2.17), is not always able to account for all aspects of PVDs, 

methods of numerical analysis (typically FEM) are often required for accurate 

predictions. However, considering the potential numerical challenges involved and 

uncertainty surrounding the properties and varying magnitude of the smear zones, 

comprehensive efforts of modelling isolated drains may yield limited benefits. In contrast, 

employing a simplified approach can be key for achieving effective and precise 

predictions of performance of PVD-improved soil, as emphasized by Amavasai et al. 

(2018). 

From a macro perspective, the installation of vertical drains enhances the vertical 

hydraulic conductivity of the underlying soil. As a result, it is reasonable to attempt to 

determine an approximate value for the hydraulic conductivity that encompasses both the 

influence of natural vertical drainage and the radial drainage caused by the presence of 

prefabricated vertical drains (PVDs). Chai et al. (2001) introduced an approach that 

enables the user to analyse soil that has been improved with PVDs in a similar way to the 

unimproved case. The method incorporates an equivalent vertical hydraulic conductivity, 

kve, derived through a process based on the assumption of equal average degree of 

consolidation under the initial conditions. Using to the method introduced by Carillo 

(1941) the effects of horizontal and vertical drainage are combined through the 

relationship in equation (2.18). 

a"? = 1 − (1 − a")(1 − a?) (2.18) 

where Uvr is the average degree of consolidation of drain improved soil, and Uv equals 

the average degree of consolidation in the vertical direction. The degree of consolidation 

due to radial drainage Ur should be calculated by Hansbo’s solution (1981), defined 

previously in equations (2.15) - (2.17).   

To arrive at a simple expression for equivalent hydraulic conductivity in the vertical 

direction, kve, Chai et al. (2001) proposed an approximation of Terzaghi’s general 

expression for the average degree of vertical consolidation: 

 a" = 1 − exp(−
mf") (2.19) 

 



22                      

where the time factor Tv is defined as: 

f" = �" ∙ �gh$  (2.20) 

Where  cv = coefficient of consolidation in vertical direction 

 H = vertical drainage length [m] 

 Cd = constant [-] 

 t = time [year] 

Furthermore, Chai et al. (2001) specified a number of factors that need to be considered 

to determine the value of the constant Cd. 

• Equation (2.19) is specifically utilized to determine value of kve. Once kve has been 

determined, a"  is calculated using Terzaghi’s theory for one dimensional 

problems and Biot’s theory (1941) for cases in 2D and 3D.  

• As depicted in Figure 2.13, when Uv equals 50%, equation (2.19) produces the 

same outcome as Terzaghi’s theory if the constant Cd is assumed as 3.54. 

However, equation (2.19) underestimates the average degree of consolidation for 

Uv < 50% and overestimates for Uv > 50%, with a maximum error of less than 10% 

(Chai, et al., 2001). Consequently, when converting the apparent effects of PVDs 

into kve, and ignoring the vertical drainage of natural soil, Cd = 3.54 is the most 

appropriate value.  

• It is possible minimize errors in the average degree of consolidation by accounting 

for both the vertical drainage of the natural soil as well as the radial drainage of 

the installed PVDs. However, adopting the value of Cd = 3.54 will result in the 

range of underestimation being more than half (Chai, et al., 2001).  

• The optimal value of Cd depends on the relative significance of vertical and radial 
drainage, which varies form one case to another. 

 

Figure 2.13. Influence of constant Cd on degree of consolidation (Chai, et al., 2001). 



 

 

 

  23 

As (2.19) takes the same form as (2.15) (Hansbo’s solution) the equivalent hydraulic 

conductivity in the vertical direction, kve, can be defined through a simple expression: 

 "h = #1 + 2.50$ I�gh$ " %  " (2.21) 

where all parameters are previously defined.  

For conditions where the soil stratigraphy is interpreted with multiple layers, and (2.19) 

is used to calculate kve, it can simply be assumed that the length of the drainage l equals 

the thickness H of the zone with PVDs installed. Consequently, l = H for one-way 

drainage and l = H/2 when considering two-way drainage. In a case where the soft soil 

deposit is experiencing drainage on two fronts, but the installed drains are not installed 

all the way to the permeable layer, as seen in figure Figure 2.14, one-way drainage should 

be applied.  

 

Figure 2.14. Different drainage conditions of PVD-improved soil (Chai, et al., 2001). 

Ultimately, Chai et al. (2001) highlighted the fact that one-dimensional conditions are 

used to arrive at the kve value. However, this does not mean the proposed method is only 

applicable in cases for 1D analysis. A vertical drain-improved zone hydraulic 

conductivity of kve in vertical direction and kh in horizontal direction can be used in 2D 

and 3D, depending on the requirements of the situation.  

  



24                      

2.4. Plane Strain and PVD Performance  

Typically, numerical analyses of embankments are conducted using plane strain 

conditions (Figure 2.15b) for a cross-section perpendicular to the centreline of the 

embankment. However, this approach becomes problematic when attempting to model 

the impact of PVDs, as the consolidation conditions around each drain are closer to that 

of the axial symmetry (Figure 2.15a) (Hird, et al., 1995). To incorporate the influence of 

drains, methods for matching their effect under axisymmetric and plane strain conditions 

needs to be used.  

 

 (a) (b)  

Figure 2.15. Direction of flow for PVDs in (a) axisymmetric conditions (b) plane strain conditions (Almeida 

& Marques, 2013). 

There are several methods available to numerically model the effects of PVDs in plane 

strain, including the mathematical matching procedure introduced by Hird et al. (1992) 

and the homogenisation method using equivalent vertical permeability by Chai et al. 

(2001) described in the previous section. Various techniques can be employed, but the 

key factor common to all is the need for parameters that accurately represent the physical 

performance of the vertical drains being modelled.  

One of the most important parameters that influences the consolidation rate of PVD-

improved soil is the horizontal permeability (Chai & Miura, 1999). However, there is no 

satisfactory method available to test this parameter in a laboratory. Other influential 

parameters relating to PVD performance are:  

• Diameter and spacing between drains 

• Discharge capacity (well resistance) 

• Drainage boundaries  

• Overall smear effects 



 

 

 

  25 

Except for the spacing between drains, there exist some uncertainties for quantifying 

these factors. In general, larger equivalent drain diameters result in smaller well resistance 

(greater discharge capacity) and a smaller smear effect gives a more effective vertical 

drain. The equivalent drain diameter, dw, for a band shaped drain initially relied on the 

assumption of equal drainage perimeter. However, further research has shown that the 

presence of corner effects results in a smaller equivalent diameter (Chai & Miura, 1999). 

The equivalent drain diameter, dw, depends on the width, w, and thickness, t, of the drain, 

according to equation (2.22). 

 =� = p + �2  (2.22) 

The discharge capacity of PVDs have significant impact on drain behaviour. However, 

they require experimental determination and should be included by the provider of the 

drain. Moreover, according to Chai & Miura (1999), it is reasonable to assume a circular 

boundary of the smear zone, based on the rectangular shape of the mandrel and equal area 

assumption.  

 

(a) (b) 

Figure 2.16. (a) Axisymmetric and (b) plane strain view of a PVD unit cell (Chai, et al., 1995). 

To quantify the effect of the smear zone surrounding the drains on soil permeability, two 

parameters are required: the diameter of the smear zone (ds) and the hydraulic 

conductivity ratio (kh/ks), which represents the ratio of horizontal hydraulic conductivity 

in the undisturbed zone (kh) to that in the smear zone (ks) (see illustration of parameters 

in Figure 2.16). An estimation of the diameter of the smear zone (ds) can be made through 

equation (2.27). 



26                      

 =8 = (2 �1 3)=q (2.23) 

Where dm is the equivalent diameter of the mandrel. For the value of kh/ks there are many 

uncertainties. It is possible to determine the parameter in a laboratory, although the results 

are often underestimated due to sample disturbance and sample size (Chai & Miura, 

1999). Moreover, as described in the previous section, the smear effect decreases with 

the radial distance from the drain. The value of kh/ks can be approximated by:  

  I 8 = � I 8 !
r ∙ 
s (2.24) 

Where l is determined using laboratory tests and Cf is the ratio of hydraulic conductivity 

when comparing laboratory and field values.  

2.5. Numerical Modelling of Soft Soil 

Numerical modelling provides a valuable tool for the geotechnical engineer in providing 

insights, predictions and allows for informed decision-making. It allows for explorations 

of different scenarios and evaluations of potential risks and mitigation measures, testing 

innovative solutions and assessing the long-term performance of geotechnical systems 

during the design phase.  

 

Figure 2.17. Typical loading paths associated with construction projects in urban areas (Karstunen, 2021). 

In geotechnical design, situations where we have limited control over the applied loads 

and the resulting stress paths that develop from the coupled hydro-mechanical response 

of natural soil often emerge (Karstunen, 2021). This is especially true for underground 

projects in poulated areas, as depicted in Figure 2.17., where various total stress paths 

associated with different types of construction are represented by means of stress p and 

deviatoric stress q. Naturally, it is impractical to conduct extensive testing in every single 

project for all the possible stress paths. Thus, a representative constitutive model is 

needed (Karstunen & Amavasai, 2017).  



 

 

 

  27 

A constitutive model is a generalized representation of the stress-strain relationship in 

soil when under surcharge loading (Potts, 2003). An instance familiar to most 

geotechnical engineers where a constitutive model is applied is when conducting slope 

stability analyses using the limit equilibrium method. In this method, a rigid-perfectly 

plastic behaviour is assumed in the soil implying it remain completely undeformed until 

a failure occurs (see Figure 2.18) (Karstunen & Amavasai, 2017). Furthermore, elasto-

plastic perfectly plastic constitutive models include, i.e., the Mohr Coulomb model. The 

model assumes a purely linear elastic response until a point of failure is reached after 

which perfect plastic deformations are calculated, with the points being the principal 

stresses that define the yield surface.  

 

Figure 2.18. Various classifications of elasto-plastic models (Karstunen & Amavasai, 

2017). 

Rate-independent elasto-plastic constitutive models encompass several fundamental 

properties, including: an elastic law, yield surface, flow rule and hardening law.  

An elastic law defines the stress-strain relationship under elastic conditions and 

determines the calculation of elastic (recoverable) strains.  

The yield surface is what defines the boundary of small, recoverable (elastic) strains, and 

the larger irrecoverable (plastic) strains (Phillips & Sierakowski, 1965). Mathematical 

formulations utilized to describe the yield surfaces vary among different models.  

A flow rule is essential as it determines the direction of the stress path during plastic flow, 

thus, defining the magnitude of calculated incremental strains. In generalized elasto-

plastic models, the ratio of incremental strains varies depending on the type of loading 

must be defined accordingly (Amavasai, et al., 2017).  

As described previously in section 2.1, soft soils commonly experience substantial 

contraction or volumetric reduction when under surcharge loading. Hence, an elasto-

plastic perfectly plastic constitutive model proves totally inadequate for accurately 

representing the stress-strain behaviour of soft clays that are normally consolidated or 

lightly over consolidated. For soft soil conditions, models that exhibit an elasto-plastic 



28                      

hardening or softening behaviour are more appropriate (see Figure 2.18) (Karstunen & 

Amavasai, 2017).  

Hardening laws characterize the evolution and size of the yield surface based on the 

increments of plastic strains. The hardening models have the capability to provide 

explanations for several observed occurrences in soil, including the influence of stress 

history on soil stiffness and the increase of undrained shear strength during the 

consolidation process (Ti, et al., 2009). One example of such models is the hardening soil 

model. On the other hand, if the effect of degradation of mobilised shear strength in the 

soil needs to be accounted for, as would be necessary for sensitive soft clays, models that 

enable strain softening are required (see Figure 2.18).  

Rate-dependent (creep) models, such as the Creep-SCLAY1S model explored in this 

thesis, are built on similar concepts but with but with modifications. The most significant 

distinction being that it does not have a purely elastic region, like the Mohr-Coulomb or 

the Hardening Soil model. Creep-SCLAY1S is a rate-dependent enhancement of the 

Modified Cam Clay (MCC) model. Instead of a yield surface, the Creep-SCLAY1S 

model, and similar rate-dependent models such as Soft Soil Creep, introduce the idea of 

a Normal Compression surface (NCS). The surface constitutes the boundary between 

small, recoverable, strains and more significant, irrecoverable creep strains. This concept 

will be elaborated on in the following section.  

2.6. Creep-SCLAY1S Model  

Creep-SCLAY1S is a constitutive model for soft clays capable of simulating features of 

soil behaviour like anisotropy, structural degradation, and rate-dependency (Amavasai, 

et al., 2017). The model is a further developed version of the Creep-SCLAY1 model 

introduced through a collaboration between, Chalmers University of Technology, Plaxis 

bv and NGI (Karstunen & Amavasai, 2017). Creep-SCLAY1 originated from the 

Modified Cam Clay model but was further extended on the ideas by Wheeler et al. (2003) 

and Karstunen et al. (2005), with adaptations for application on sensitive natural clays. 

For the sake of simplicity, the model is mathematically formulated in the triaxial stress 

space, see Figure 2.19. Therefore, it can only be used to model samples vertically cut 

form the soil deposit (cross-anisotropic) which are subjected to triaxial or oedometric 

loading (Sivasithamparam, et al., 2015).  



 

 

 

  29 

 

Figure 2.19. General stress space of Creep-SCLAY1S model (Karstunen, et al., 2013) 

The fundamental assumption in the Creep-SCLAY1S model is that a purely elastic region 

does not exist (Amavasai, et al., 2018). Consequently, viscoplastic (creep) deformations 

take place at all stress levels. The total strain rate is mathematically represented through 

an additive law combining both the elastic and viscoplastic components, as demonstrated 

in equations (2.25) & (2.26) (Sivasithamparam, et al., 2015). 

 /t" = /t"h + /t"@ (2.25) 

  /tu = /tuh + /tu@ (2.26) 

where ε equals strain and dot over symbol refers to rate (differentiation with respect to 

time). The superscript e refers to the elastic component and c to the viscoplastic 

component. Subscripts v refer to the volumetric part and q refer to the deviatoric part. 

 

Figure 2.20. Constitutive yield surfaces for the Creep-SCLAY1S model (Tornborg, et al., 2021). 



30                      

The model comprises thee yield surfaces which are defined simplistically in the triaxial 

stress space, see Figure 2.20 (Amavasai, et al., 2017). The Normal Consolidation Surface 

(NCS) is analogous to, and serves as, a boundary surface between small and large creep 

strains. Here, the apparent pre-consolidation pressure of natural clay is used to determine  

the size of the surface (denoted by p′v in Figure 2.20). The second surface CSS, or the 

Current Stress Surface, represents the present effective stress state of the soil. 

Consequently, the modified over-consolidation ratio (OCR*) is determined by the ratio 

between the size of the CSS (defined by w′hu in Figure 2.20) and the size of the NCS. To 

incorporate the effects of structural degradation, an Intrinsic Compression Surface (ICS) 

is introduced (Sivasithamparam, et al., 2015). The size of the ICS (denoted as w′qx in 

Figure 2.20) is defined and related to the size of the NCS using equation (2.27). Moreover, 

NCS, ICS and CSS have similar orientation and shape and are defined using equation 

(2.28). 

where w′ represents the mean effective stress and l the deviatoric stress. y represents the 

current amount of bonding present in the soil. The term w′8 can be substituted with w′q w′hu  w′qx  to define the respective surface, see Figure 2.20. 7 is a scalar state variable 

which corresponds to the orientation of the yield surface in the simplified triaxial stress 

space, see, indicating the change in soil anisotropy (Karstunen & Amavasai, 2017). �(z,) represents the formulation of the modified Lode angle of the critical state, which 

governs the inclination of the critical state in triaxial compression (Mc) and extension 

(Me) (see Figure 2.21). By incorporating a Lode angle dependency, a smooth yield surface 

is obtained by avoiding sharp corners and thus simplifies numerical computations 

(Sivasithamparam, et al., 2015). The formulation of (2.29) the critical slope dependent 

Lode angle is expressed as: 

 �(z,) = �@ # 2{|
1 + {| + (1 − {|) sin 3z,%~/|

 (2.29) 

and 

 sin 3z, = − �3√32 (��),(�$),�/$� (2.30) 

In Figure 2.21 the Lode angle is depicted for variations in the value of m, where m is 

defined as Me/Mc. Further, (�$), and (��), define invariants of the modified deviatoric 

stress tensor. 

w′q = w′qx(1 + y) (2.27) 

w′8 = w′ + (l − 7w′)$
(�(z,)$ − 7$)w′ (2.28) 



 

 

 

  31 

 

Figure 2.21 Lode angle dependency of the stress state in Creep-SCLAY1S model in � -plane 

(Sivasithamparam, et al., 2015). 

Three different hardening laws are accounted for in the Creep-SCLAY1S model 

(Karstunen & Amavasai, 2017). The first rule of isotropic hardening is related to the 

variation of the intrinsic isotropic pre-consolidation pressure w′qx  as well as the 

viscoplastic volumetric strain rate /t"@ though equation (2.31). 

 w′q = w′qx�x∗ − 	∗ /t"@ (2.31) 

where �x∗ is the modified compression index and represents the stiffness in the soil, with 

the subscript i indicating an intrinsic material state, derived at large strains where 

complete loss of structure has occurred. 	∗ is the modified compression index. 

The second hardening law express the variation of the orientation of the reference surface 

due to the viscoplastic strain rate as formulated by (Leoni, et al., 2008), see equation 

(2.32). 

 7tm = � �E3�4 − 7mF 〈/t"@  〉 + �m ��3 − 7m� /tm@  ! (2.32) 

where � is the stress ratio (� = l/w′) and � and �m are model constants that are related 

to evolution of anisotropy. �  controls absolute effectiveness of rotational hardening 

while �m controls the relative effectiveness of rotational hardening due to viscoplastic 

strain rate in the deviatoric plane (Amavasai, et al., 2017). 

The third hardening rule addresses the degradation of bonding to the increase of 

viscoplastic strains. The variation in the parameter y  is determined by the rates of 

volumetric and deviatoric viscoplastic strain, and is influenced by the two parameters �" 

and �m as expressed in (2.33) (Karstunen & Amavasai, 2017). �" governs the absolute 

rate of structural degradation while �m  regulates the impact of deviatoric viscoplastic 

strain rate on relative effectiveness of structural degradation. 



32                      

 yt = �"(�0 − y�|/t"@| + �m�0 − y�|/tm@|) = −�"y(|/t"@| + �m|/tm@|) (2.33) 

In the Creep-SCLAY1S model, an associated flow rule is assumed, as is reasonable due 

to evolution of anisotropy being included in the formulation (Sivasithamparam, et al., 

2015). Thus, the creep related strain rates are defined as (2.34), where Λt  is the viscoplastic 

multiplier, defined in (2.35), incorporated to capture the rate dependent behaviour (creep) 

in the soil (Grimstad, et al., 2010)  

 /tx�@ = Λt �w′hu��′x�  (2.34) 

Λt = �x∗� # w′hu(1 − y)w′qx%
� ��@$ − 7�C��$

�@$ − ��C��$ �  and � = �x∗ − 	x�x∗  (2.35) 

where �x∗  is the intrinsic modified creep index, corresponding to intrinsic material 

properties as all internal structure of the soil is erased. � is the reference time which 

describes at what duration (time increment) the incremental loading laboratory test, used 

for determining the pre-consolidation pressure, is conducted at. 7�C��  is an expression of 

the inclination of the constitutive ellipses that correspond to the initial �; conditions, 

while ��C�� refers to its stress ration while in the normally consolidated state.  

As evident, the Creep-SCLAY1S model is designed to comprehensively address multiple 

aspects of natural soil behaviour, which necessitates the utilization of an extensive array 

of input parameters. In the following section the individual parameters used in the model 

are described.  

  



 

 

 

  33 

2.6.1. Parameters 

The following sections includes a description of the various input parameters for the 

Creep-SCLAY1S model. In Table 2.4 a summary of the parameters is presented along 

with required laboratory tests for determination of the parameter.  

Table 2.4 Summary of input parameters and required laboratory test. 

Parameter 
type 

Parameter Symbol Required laboratory test 

Conventional 
parameters 

Modified swelling index κ* Oedometer IL or CRS test 
Poisson’s ratio v’ Triaxial test 

Modified intrinsic 
compression index 

λi* Oedometer IL or CRS test 

Stress ratio at critical state in 
triaxial compression 

Mc Triaxial compression test 

Stress ratio at critical state in 
triaxial extension 

Me Triaxial extension test 

Anisotropic 
parameters 

Absolute effectiveness of 
rotational hardening 

ω Triaxial extension test 

Relative effectiveness of 
rotational hardening 

ωd Calculated (see equation (2.43) 

Initial anisotropy α0 Calculated (see equation (2.42) 

Bonding and 
destructuration 

parameters 

Absolute rate of 
destructuration 

ξv 
Back calculated from Triaxial 

and IL/CRS test 
Relative rate of 
destructuration 

ξd Back calculated from Triaxial 
and IL/CRS test 

Initial bonding χ0 Estimated using sensitivity (St) 

Viscous 
parameters 

Modified intrinsic creep index µi* Oedometer IL (creep) test 
Reference time (days) τ Oedometer IL average time step 

Initial stress 
parameters 

Pre-overburden pressure POP Oedometer IL or CRS test 
Over consolidation ratio OCR Oedometer IL or CRS test 

Lateral earth pressure at rest K0 K0-triaxial test or calculated 
(see equation (2.12) 

Lateral earth pressure at rest 
for normally consolidated 

state 

�;JK Calculated (see equation (2.13) 

2.6.1.1. Initial stress state parameters 

The apparent pre-consolidation pressure is a crucial parameter in geotechnical analysis 

and has a large influence on predictions of creep models in general (Karstunen, 2021). As 

described in section 2.1.3 the value of �′@ is affected by anthropological and geological 

processes and is thus very site-specific. For the Creep-SCLAY1S model the interpretation 

is best done in linear scale, as anisotropy may influence yielding when plotting in a semi-

logarithmic scale (Karstunen & Amavasai, 2017). Moreover, as touched upon in sections 

2.1.3 and 2.1.4, the derived values of �′@ from laboratory tests is severely influenced by 

strain rate effects and sample disturbance and, consequently, as is the results of the 

conducted prediction. Thus, for the Creep-SCLAY1S model, it not advised to use CRS 



34                      

tests when deriving the pre-consolidation pressure, rather, incremental loading tests (IL) 

are recommended (Karstunen & Amavasai, 2017). After determination of �′@ POP and 

OCR can be calculated according to equations (2.10) and (2.11). Moreover, either a 

constant POP or a constant OCR should be selected as input for the model. 

The values of the coefficient of lateral earth pressure at rest for the normally consolidated 

state, �;JK, and �; for the over consolidated state, are estimated with the friction angle at 

critical state LM@, using previously defined equations (2.13) and (2.14). In this case, the 

values of �;  and �;JK are directly dependant on the value of �@ . However, these can 

also be calibrated and, if available, determined using advanced K0-triaxial tests (Gras, et 

al., 2017). 

2.6.1.2. Conventional parameters  

Five of the total 10 parameters for the Creep-SClay1S model that can be defined using 

standard laboratory test data have similarities with the Modified Cam-Clay model 

(Sivasithamparam, et al., 2015). The conventional isotropic soil constants used in the 

model include �′, �x∗, 	∗, �@ and �h.  

Poisson’s ratio for unloading - reloading, denoted as �M, is a purely elastic soil constant. 

In the case of soft soils, like clay, it is commonly assumed at a constant value ranging 

between 0.1 and 0.2 (Karstunen & Amavasai, 2017).  

 

Figure 2.22. Illustration of determination of stiffness parameters (a) �∗,  ��∗,  	∗and (b) 
� and 
� (Gras, et 

al., 2017). 

In the Creep-SCLAY1S model, one of the parameters relating to the stiffness in the soil 

is the modified intrinsic compression index, �x∗ . This can be determined from an 

oedometer IL test but using reconstituted samples, or analogously to the similar modified 

compression index, �∗, but from a high enough stress state in the test that all inter-particle 

bonds are erased (see Figure 2.22) (Karstunen & Amavasai, 2017). The modified swelling 

index, 	∗, also relating to the stiffness of the soil, is not defined as a constant used for 

natural clays with high sensitivity. However, for the purpose of modelling the highest 

gradient from an incremental loading test can be used (Sivasithamparam, et al., 2015). 



 

 

 

  35 

The parameters �∗ and 	∗ correspond to a radial stress path in a wM − l plane as they are 

determined in a semi-logarithmic /" − ln(wM) scale (see Figure 2.22 ), where /" is the 

volumetric strain and p’ is the mean effective stress. Moreover, as seen in Figure 2.22, 

they can be related to their 1D equivalents in an 6 − log(�M") (or /" − log(�M")) plot, 

i.e., the compression index, 
@, and swelling index 
8 respectively. The relationship is 

defined by equations (2.36)-(2.38).  

 
@ = Δ6Δ log( �′") 
8 = Δ6Δ log( �′") (2.36) 

�∗ = λ1 + 6; 	∗ = κ1 + 6; (2.37) 

�∗ = 
@2.3(1 + 6;) 	∗ ≈ 2 
82.3(1 + 6;) (2.38) 

where 6; is the initial void ratio.  

The parameter M denotes the stress ratio at critical state (l/w′), where  �@ correspond to 

the critical state line in triaxial compression and �h  for triaxial extension. �@  is 

determined using anisotropically consolidated undrained triaxial tests in compression 

(CAUC). In, i.e., excavation problems, it is preferable to have an additional test with 

shearing in extension (CAUE) for determination of �h (Karstunen, 2021). The method 

for determination of �@ and �h are presented in equations (2.39) and (2.40) (Muir Wood, 

1990). 

�@ = 6 ��DL′@3 − ��DL′@  (2.39) 

�h = 6 ��DL′@3 + ��DL′@  (2.40) 

where φ’c is the friction angle at critical state. 

If triaxial extension tests are unavailable, �h, can be calculated using �@, by assuming 

an equal friction angle in extension and compression by using the Mohr-Coulomb failure 

criterion, see equation (2.41). 

��D L′@ = 3 �h6 − �h (2.41) 



36                      

2.6.1.3. Anisotropic parameters 

During deposition, sedimentation, consolidation history and any subsequent straining, 

natural soft clays develop a substantial degree of anisotropy  (Yin & Karstunen, 2011). 

This has a significant influence on the stress-strain behaviour of soft clays, particularly in 

terms of their viscous behaviour and deformations. Consequently, this need to be 

considered in analysis and predictions related to the mechanical response of the soil 

(Leoni, et al., 2008). The Creep-SCLAY1S model accounts for this phenomenon though 

including the state parameter 7; that characterise the anisotropy of the soil deposit by 

describing the initial rotation of the yield surface. An approximation for the initial rotation 

can be expressed using equation (2.42) 7; depends on �@ and the normally consolidated 

stress ratio ��C (Wheeler, et al., 2003).  

7; = ��C$ + 3��C − �@$3  where  ��C = 3(1 −  �;JK)
(1 + 2�;JK)  (2.42) 

If advanced �;-triaxial tests are not available, �;JK can be determined by Jaky’s formula, 

see equation (2.13). In generalised 2D and 3D form the scalar 7;  is replaced by a 

deviatoric fabric tensor that is analogous to the deviator stress tensor (Wheeler, et al., 

2003). 

Furthermore, the value of �m determines the relative effectiveness of rotational hardening 

and depends on �@ and ��C . It can be evaluated using equation (2.43) (Wheeler, et al., 

2003). 

�m = 38
�4�@$ − 4��C$ − 3��C 

���C$ − �@$ + 2��C   (2.43) 
 

The initial value obtained for the parameter representing the absolute effectiveness of 

rotational hardening, �, can be determined using equation (2.44). � is also possible to 

calibrate through simulation of a triaxial test that is anisotropically consolidated to in-situ 

conditions and sheared to failure in extension (Karstunen & Amavasai, 2017).  

� ≈ 1(�x∗ − 	∗) 0D #10�@$ + 27;�m�@$ + 27;�m % (2.44) 

where other parameters are previously defined.  

2.6.1.4. Bonding and destructuration  

In addition to anisotropy, it is common for natural soils to display some form of apparent 

bonding. Furthermore, as natural clays undergo deformation, the initial apparent bonding 

gradually diminishes. Thus, at significant strains, the soil begins to exhibit behaviour 

similar to fully reconstituted material, see Figure 2.23 (Yin & Karstunen, 2011). In the 



 

 

 

  37 

Creep-SCLAY1S model the effects of bonding and destructuration is incorporated using 

a scalar quantity, y, representing the amount of bonding between particles. y; is a state 

parameter defining the initial amount of bonding in the soil, relating intact soil samples 

to reconstituted samples where all bonding of the soil is erased, see Figure 2.23 (Yin & 

Karstunen, 2011). The initial amount of bonding is expressed using the sensitivity of the 

soil through: 

where he sensitivity ¡B represents the relationship between the undisturbed peak strength 

and the remoulded strength of the soil and can be determined using various measurement 

methods. Some common approached include field or laboratory vane tests and the 

Swedish fall-cone test (Gras, et al., 2017). 

  

Figure 2.23. Relationship between intact and reconstituted soil samples of sensitive clay (Yin & Karstunen, 

2011) 

Furthermore, the model parameters �" and �m govern the degradation of bonds in the soil 

due to volumetric and deviatoric strains respectively. However, these parameters are not 

derived directly from standard laboratory test and require optimisation.  

2.6.1.5. Viscous parameters 

The intrinsic modified creep index, �x∗, is determined by the inclination of the curve in 

the /" − 0D(t) plane at the end of the consolidation phase in an oedometer test, see Figure 

2.24. The notation i determines it is an intrinsic parameter and should subsequently be 

derived at large stresses, or reconstituted samples, where all internal structure of the soil 

is erased (Gras, et al., 2017).  

y; = ¡B − 1 (2.45) 



38                      

 

Figure 2.24. Procedure for determination of ��∗ at high stress levels where all soil structure is erased.  

Moreover, it is also possible to derive the parameter �x∗ using the intrinsic secondary 

compression index 
,x  (corresponding to high enough stress levels) described in section 

2.1.1 using the relation: 

�x∗ = 
,x2.3(1 + 6;)  (2.46) 

Where 
,x = Δ6/Δlog (�) 

The reference time, �, represents the duration, in days, of the load step in the oedometer 

test that is conducted to determine the initial pre-consolidation pressure. If the test is done 

using 24-hour loads step the reference time is set to 1 (Gras, et al., 2017). 



 

 

 

  39 

3. Ballina Trial Embankments 

The case study for this thesis relates to the Ballina trial embankment. Ballina is a test site 

with full-scale trial embankments constructed at the National Field-Testing Facility 

(NFTF) for soft soils in Ballina, New South Wales. The concept was brought forward by 

the Ballina Bypass Alliance after facing challenges during the construction of a nearby 

highway. Over a span of 3 years, a maximum settlement of 6.4 m settlements occurred 

(up to 14 m embankment fill) (Kelly, et al., 2017). Currently, there is around 150 km of 

highway under construction in the general area of Ballina, of which about 25 km consists 

of soft soils. Accurately predicting the settlement, the rate at which it occurred and the 

horizontal movements in the soil proved to be difficult. This led to the field-testing facility 

being established after the Australian Research Council Centre of Excellence for 

Geotechnical Science and Engineering (CGSE) took up on the idea. The overall 

motivation of the research project was to improve the process of design and construction 

of infrastructure on naturally deposited soft soil (Pineda, et al., 2019). The site in Ballina 

offered an ideal location for a test facility due to its convenient access, favourable ground 

conditions, and close proximity to ground conditions of the planned projects.  

 

Figure 3.1. Plan view of the Ballina National Field-Testing Facility including location of in-situ tests 

conducted at the site (Kelly, et al., 2017). 

Two embankments were built at the site in 2013. A plan view with location of conducted 

in-situ tests and boreholes can be seen in Figure 3.1. One of the embankments was 

constructed with conventional PVDs (Prefabricated Vertical Drains), as well as 

biodegradable jute drains, and the other without any drains installed (Kelly, et al., 2017). 

In this thesis, both embankments will be modelled. However, only the embankment 

modelled with drains is compared with measurement data (class C prediction). The 



40                      

embankment without drains will be modelled as a class A prediction, as there are 

currently no published results available.  

Before construction, soil samples of high quality were obtained and subjected to advanced 

laboratory testing and the site was instrumented extensively. Installed instruments 

gathered data on deformations in vertical and horizontal direction as well as pore 

pressures and vertical- and horizontal soil pressures. Measurements were recorded at the 

site for