Revised Version PhD Thesis Defended in public at Aalborg University 3 May 2016 Sarah Firouzianbandpey Department of Civil Engineering, The Faculty of Engineering and Science, Aalborg University, Aalborg, Denmark River Publishers 9788793379947 The present PhD thesis, titled “Reliability-based design of wind turbine foundations—Geotechnical site assessment”, is submitted as a partial fulfilment of the requirements for the Danish PhD degree. The work has been carried out in the period October 2011 to September 2014 at the Department of Civil Engineering, Aalborg University, Denmark, under the supervision of Prof Lars Bo Ibsen and Dr Lars Vabbersgaard Andersen. Also there was an extensive collaboration with Prof D. Vaughan Griffiths in the Department of Civil Engineering, Colorado School of Mines, USA. The PhD thesis consists of two parts: Part I deals with applications of CPTu / SCPT in-situ testing methods in subsurface investigations and uncertainty regarding different models to predict the soil type from cone data. Different empirical charts have been investigated and verified as a case study in different soil types. Part II deals with the effects of soil variability on estimating of design parameters and final cost for wind turbine foundations. The spatial correlation length of cone data was estimated and employed the identification of soil parameters at unsampled locations. The thesis is based on the following scientific papers with a collaboration of other authors. Firouzianbandpey, S., Ibsen, L.B., Andersen, L.V. (2012). CPTu-based Geotechnical Site Assessment for Offshore Wind Turbines—a Case Study from the Aarhus Site in Denmark. In Twenty-second International Offshore and Polar Engineering Conference, Rhodes, Greece, pp. 151-158. Firouzianbandpey, S., Nielsen, B.N., Andersen, L.V., Ibsen, L.B. (2013). Geotechnical Site Assessment by Seismic Piezocone Test in the North of Denmark. Seventh International Conference on Case Histories in Geotechnical Engineering, Wheeling, IL. Missouri University of Science and Technology, 2013. Paper no. 2.34. Firouzianbandpey, S., Ibsen, L.B., Andersen, L.V. (2014). Estimation of soil type behavior based on shear wave velocity and normalized cone data in the north of Denmark. 3rd International Symposium on Cone Penetration Testing, Las Vegas, Nevada, USA. Pp. 621-628. Firouzianbandpey, S., Griffiths, D. V., Ibsen, Lars Bo., Andersen, and L. V. (2014). Spatial correlation length of normalized cone data in sand: case study in the north of Denmark. Canadian Geotechnical Journal, Vol. 51, No. 8, pp. 844-857. Firouzianbandpey, S., Ibsen, L.B., Griffiths, D.V., Vahdatirad, M. J., Andersen, L.V., Sørensen, J. D. (2014). Effect of spatial correlation length on the interpretation of normalized CPT data using a Kriging approach. Journal of Geotechnical and Geoenvironmental Engineering (ASCE). Copies of all publications are enclosed in the thesis. I would like to thank my supervisor Professor Lars Bo Ibsen for giving me the opportunity to work on this PhD thesis and for his counselling and support during the experiments and studies. I am especially thankful to Dr Lars Vabbersgaard Andersen. If he had not served as my co-advisor and had not encouraged me throughout this dissertation process, this dissertation could not have been completed. I thank him for providing me with the opportunity to pursue this research. I would also like to warmly acknowledge Prof D. Vaughan Griffiths for providing guidance and suggestions for me to improve this dissertation. Among many peoples who have been helpful in the compilation of this dissertation, I would like to extend a hearty thanks to the technical staff at the Laboratories at the Department of Civil Engineering, Aalborg University for their assistance with the experimental work related to Part I. Finally, I express my great appreciation to my family for their faith and encouragement. They deserve special mention for their inseparable support and prayers. Words fail me to express my appreciation to my husband, Javad, for his unconditional love, assistance and patience during the last three years. Sarah FirouzianbandpeyAalborg, December 2014 With industrialization taking off in the 18th century, a dramatic increase of carbon dioxide emission began due to burning of fossil fuels. The heat-trapping nature of carbon dioxide causes global warming resulting in major concern about climate change as w ell as in an increased demand for more reliable, affordable, clean and renewable energy. Wind turbines have gained popularity among other renewable energy generators by having both technically and economically efficient features and by offering competitive production prices compared to other renewable energy sources. Therefore, it is a k ey green energy technology in breaking the fossil fuel dependency. The costs of foundations for offshore wind turbines typically amount to 20-30% of the total wind turbine budget. Thus, an optimized design of these foundations will improve the cost effectiveness by matching a suitable target reliability level. The overall aim of the present PhD thesis is to facilitate a low-cost foundation design for future offshore wind farms by focusing on the geotechnical site assessment. First, a number of well-established techniques for soil classification based on cone penetration test (CPT) data have been investigated for a local case in order to estimate the inherent uncertainties in these models. For the purpose of verification and prediction of the best method for the region, a comparison was made with laboratory test results on samples retrieved from boreholes at the site. In addition to this, several seismic CPTs were performed in sand and clay in order to estimate the small-strain shear modulus of the soil as a key parameter in analysis and design of foundations, and the soil type of the region was estimated based on this value. Furthermore, the shear moduli obtained from the seismic tests were compared with moduli estimated from cone data using different empirical relations. The later part of the thesis concerns the assessment of the spatial correlation lengths of CPTu data in a sand layer. Results from two different sites in northern Denmark indicated quite strong anisotropy with significantly shorter spatial correlation lengths in the vertical direction as a result of the depositional process. The normalized cone resistance is a better estimator of spatial trends compared to the normalized friction ratio. In geotechnical engineering analysis and design, practitioners ideally would like to know the soil properties at many locations, but achieving this goal can be unrealistic and expensive. Therefore, developing ways to determine these parameters using statistical approaches is of great interest. This research employs a random field model to deal with uncertainty in soil properties due to spatial variability by analysing CPTu data from a sandy site in northern Denmark. Applying a Kriging interpolation approach gave a best estimate of properties between observation points in the random field, and the influence of spatial correlation length on the results was investigated. Results show that a longer correlation length reduces the estimator error and results in more variation in the estimated values between the interpolated points. Med industrialiseringens start i det 18. århundrede begyndte en dramatisk forøgelse af carbondioxid-emission forårsaget af afbrænding af fossile brændstoffer. Carbondioxids varmefangende karakter forårsager global opvarmning, hvilket resulterer i stor bekymring for klimaforandring såvel som øget efterspørgsel på mere pålidelig, prisbillig og ren vedvarende energi. Vindmøller er blevet populære blandt de andre vedvarende energigeneratorer ved både at have teknisk og økonomisk ydeevne og ved at tilbyde konkurrencedygtige produktionspriser sammenlignet med andre vedvarende energikilder. Derfor er det en vigtig grøn-energiteknologi, der kan tilendebringe afhængigheden af fossile brændstoffer. Omkostningerne ved fundamenter til havvindmøller ligger typisk omkring 20-30% af det totale budget for vindmøller. Af denne årsag vil et optimeret design af fundamenterne forbedre omkostningseffektiviteten ved at matche et passende pålidelighedsniveau. Det overordnede mål for denne ph.d.-afhandling er at facilitere et billigt fundamentdesign for fremtidens havbaserede vindmølleparker ved at fokusere på den geotekniske bedømmelse af området. Først er en række veletablerede teknikker til klassifikation af jord baseret på CPT (cone penetration test) data undersøgt for en lokalitet i Nordjylland. Formålet er at estimere de iboende usikkerheder i klassifikationsmetoderne. En sammenligning blev lavet med laboratorietestresultater på prøver, der er taget fra boringer ved stedet, for herigennem at kunne identificere og verificere den bedste metode for lokaliteten. Desuden er adskillige seismiske CPT-forsøg blevet udført i sand og ler til estimering af aflejringernes forskydningsmodul ved lavt tøjningsniveau. Denne modul er en vigtig parameter i analysen og designet af fundamenter, og typen af aflejringer på lokaliteten blev estimeret på baggrund af denne værdi. Ydermere blev forskydningsmoduler fundet ud fra de seismiske test sammenlignet med modulerne estimeret ud fra CPT data ved anvendelse af forskellige empiriske relationer. Den sidste del af afhandlingen omhandler bedømmelsen af de stedslige korrelationslængder af CPT-data i et sandlag. Resultaterne fra to forskellige steder i det nordlige Danmark indikerede en ret kraftig anisotropi med betydelig kortere korrelationslængder i den vertikale retning som et resultat af aflejringsprocessen. Den normaliserede spidsmodstand giver et bedre mål for de stedslige variation sammenlignet med den normaliserede friktionsratio. I geoteknisk analyse og design vil den udførende part ideelt set gerne kende jordens egenskaber så mange steder som muligt, men opnåelse af et sådant kendskab kan være urealistisk og bekosteligt. Derfor er udviklingen af statistiske metoder til fastlæggelse af disse parametre af stor interesse. Denne forskning benytter en stokastisk-felt-model til at behandle usikkerheder i jordens egenskaber grundet stedslig variation ved at analysere CPT data fra en sandforekomst i det nordlige Danmark. Brug af Kriging, en avanceret interpolationsmetode, har givet det bedste estimat af egenskaberne mellem observationspunkterne i det stokastiske felt, og indflydelsen på resultaterne af den stedslige korrelationslængde blev undersøgt. Resultaterne viser, at en større korrelationslængde reducerer fejlen på estimatet og resulterer i mere variation af de estimerede værdier mellem de interpolationspunkter. Firouzianbandpey, S., Ibsen, L.B., Andersen, L.V. (2012). CPTu-based Geotechnical Site Assessment for Offshore Wind Turbines—a Case Study from the Aarhus Site in Denmark. In Twenty-second International Offshore and Polar Engineering Conference, Rhodes, Greece, pp. 151-158. Firouzianbandpey, S., Nielsen, B.N., Andersen, L.V., Ibsen, L.B. (2013). Geotechnical Site Assessment by Seismic Piezocone Test in the North of Denmark. Seventh International Conference on Case Histories in Geotechnical Engineering, Wheeling, IL. Missouri University of Science and Technology, 2013. Paper no. 2.34. Firouzianbandpey, S., Ibsen, L.B., Andersen, L.V. (2014).Estimation of soil type behavior based on shear wave velocity and normalized cone data in the north of Denmark. 3rd International Symposium on Cone Penetration Testing, Las Vegas, Nevada, USA. pp. 621-628. Paper no. 2-35. Firouzianbandpey, S., Griffiths, D. V., Ibsen, Lars Bo., Andersen, and L. V. (2014). Spatial correlation length of normalized cone data in sand: case study in the north of Denmark. Canadian Geotechnical Journal, Vol. 51, No. 8, pp. 844-857. Firouzianbandpey, S., Ibsen, L.B., Griffiths, D.V., Vahdatirad, M. J., Andersen, L.V., Sørensen, J. D. (2014). Effect of spatial correlation length on the interpretation of normalized CPT data using a Kriging approach.Journal of Geotechnical and Geoenvironmental Engineering (ASCE). As the fastest growing source of electricity generation in the world, wind power offers many benefits in the way of reducing consumption of fossil fuels. Even though the offshore wind turbine has fulfilled many commitments in the industry, many political, economic and technical challenges are still against this technology. In this regard, the soil-foundation part plays an important role. In this chapter, a brief overview of the geotechnical aspects of site investigations and degree of reliability in design of wind turbine foundations is presented with providing the challenges and motivations in this field.

The world is now concerned about climate change due to the dependence on coal, oil and gas. This increases the demand for more domestic, sustainable and largely untapped energy resources as an alternative to fossil fuels. Today, the modern offshore wind turbine is the most interesting source for generating renewable energy and a key technology in achieving the green energy and climate goals in the future. Europe is the world leader in offshore wind power, with the first offshore wind farm being installed in Vindeby, Denmark in 1991. So as a pioneer in offshore wind power, Danish energy policy attempts to support the development of the offshore wind industry by 2050 including a huge investment plan to supply 50% of electricity consumption by wind power up to 2020. Investment in EU wind farms was between €13 billion (bn) and €18 bn. Onshore wind farms attracted around €8 bn to €12 bn, while offshore wind farms accounted for €4.6 bn to €6.4 bn. Indeed, lower installation cost causes that a great amount of wind turbines are located onshore. As indicated in Figure 1-1, in terms of annual installations Germany was the largest market in 2013, installing 3,238 MW of new capacity, 240 MW (7%) of which was offshore. The UK came in second with 1,883 MW, 733 MW (39%) of which was offshore, followed by Poland with 894 MW, Sweden (724 MW), Romania (695 MW), Denmark (657 MW), France (631 MW) and Italy (444 MW). This high growth in the installed capacity of offshore wind turbines by the EU committee brings many challenges in the field of engineering and science. Figure 1-1 Figure 1-2 Also as illustrated in Figure 1-2, the annual and cumulative offshore wind installations have increased in the last few years. This increased rate in the installed capacity of offshore wind turbines brings many challenges in civil and geotechnical engineering. Particularly, an inevitable factor against this way is the cost of wind turbines and in particular their foundations which account for around one third of the total cost of a wind farm.

The nature of the ground has an inevitable influence on the construction procedure. Long term geological processes and weathering sculpt the terrain and reduce rock to sand, clay and other types of soils. These geological processes erode the higher ground and others leave complex, deposited layers of sand and clay. Together the types of rock and landform shaping processes determine the nature, strength and physical shape of the ground. Therefore, subsoil evaluation and site characterization is important for the planning and erection of wind turbines. Foundation work makes up a relatively large part of the overall cost of a wind farm. Detailed information about a site may have a significant influence on the optimization of the foundation design and can reduce the development costs. State-of-the-art spatial geophysical field methods (e.g. magnetics, side scan, echo-sounding and seismic) are combined with direct and indirect in-situ exploring methods (e.g. drillings and Cone Penetration Tests (CPT)) and the results are used to obtain material properties to be applied in computational models (e.g. finite element method).

The Cone Penetration Test (CPT) and its enhanced versions (piezocone-CPTu and seismic-SCPT) are in-situ testing methods with various applications in a wide range of soils. During the test, a cone mounted on a series of rods is pushed into the ground at a constant rate and continuously measures the resistance to penetration of the cone and of a surface sleeve surrounding the lower end of rod. Among other in-situ testing methods the CPTu has the advantages of fast and continuous profiling, being economical, repeatable and providing reliable data (not operator-dependent) and having a strong theoretical basis for interpretation of the geotechnical engineering properties of soils and delineating soil stratigraphy. Figure 1-3 shows a schematic view of a cone penetrometer. The total force acting on the cone, Qc, divided by the projected area of the cone, Ac, produces the cone resistance, qc. The total force acting on the friction sleeve, Fs, divided by the surface area of the friction sleeve, As, is the sleeve friction, fs. A piezocone also measures pore water pressure, usually just behind the cone in the location u2. Figure 1-4 indicates a typical result of a sounding profile during the test. Figure 1-3

Seismic piezocone penetration test (SCPTU) is a development of CPT by integrating a geophone in the cone. The geophone measures the acceleration generated by a hammer impact on a steel plate on the ground surface. A polarized shear wave is generated on the ground surface and the travel time is measured for the shear wave for a known distance to the geophone down in the borehole. This can be regarded as a down-hole test and provides shear wave velocity measurements simultaneously with measurements of tip resistance (qc), sleeve friction ( fs ) and pore pressure ( u ). Determination of shear wave velocity ( vs ) can be used in obtaining the soil properties. Figure 1-5 illustrates the typical layout for a downhole seismic cone test. Figure 1-5

In situ soils are heterogeneous materials created by natural environmental, geologic and physical-chemical processes, which have an influence on the design parameters of the foundation in any soil structure. Actually, the properties of soils undergo changes over both space and time. In other words, measured soil parameters can show considerable spatial variation even within relatively homogeneous layers with the same soil type. The application of statistical analysis provides the spatial variability of a data set more accurately than otherwise determined. In order to characterize the inherent spatial variability of soils, stochastic methods may be used to incorporate the effects of spatial variability into reliability-based geotechnical design approaches. Furthermore, stochastic methods help geotechnical engineers to estimate soil properties at unsampled locations and handle uncertainties related to soil properties in a more rational manner. The inherent spatial variability of soil properties is induced by the process of soil formation and depends on type of the soil. In general, statistical analysis can be divided into two parts as descriptive and inferential in nature. In the descriptive analysis, the aim is to best describe a particular data set by interpolating within the data set. This commonly happens when soil parameters are obtained at a field for which a construction is destined. The regression, using an appropriate polynomial function that demonstrates most of the variability, or best linear unbiased estimation (BLUE) are examples of descriptive techniques (see e.g. Fenton and Griffiths, 2008). Regression is most often geometry and observation based, whereas BLUE also incorporates the covariance structure of data. Inference analysis occur when soil property is estimated at any unobserved location. Hence, the word inference convey this meaning that the estimation of stochastic model parameters is based on making probabilistic statements about an entire field for which data are not available or very limited. This is essential in primary designs or when a large site is to be characterized on the basis of a small number of tests in the region.

In geotechnical engineering practice, soil properties at a specific site can be determined from laboratory tests based on a limited number of field specimens as well as in-situ tests performed in the field. As the budget of any construction project is limited, the ability to acquire data is constrained and the exact spatial variability of soil parameters remains largely unknown. Traditionally, geotechnical design is associated with a deterministic methodology based on representative soil properties regardless of the spatial variability within each soil layer. The simplified estimates of soil properties do not sufficiently supply valuable information for performing reliability analysis in geotechnical practice. Therefore, the statistical characteristics of spatial variability should be more closely examined based on stochastic methods. Designers are now demanding full reliability studies, requiring more advanced models, so that engineers are becoming interested in reasonable soil correlation structures. When uncertainties related to soil properties are presented by means of stochastic methods, the influence of spatial variability of various soil properties on structure behaviour may be assessed more accurately. This can be achieved through the use of spatial correlation structures and trend analyses. These methods provide better estimates for unsampled locations and offer valuable information regarding the uncertainty of soil properties in reliability analyses. Furthermore, the simplification due to application of partial safety factors and quantile values lead to uncertainties in current design methods. Therefore, the reliability level remains largely unknown and the design may be over-conservative. So, many initiatives are needed to reduce the expenses related to this part of the design. Before any design and analysis, geotechnical site investigations are carried out at the location of each wind turbine, commonly as cone penetration tests (CPTu) and borehole tests. The soil properties estimated from cone data as a q uantile value and used in the deterministic design of each foundation are accompanied with large statistical uncertainties. Also soil properties vary spatially from one location to another within the field and the soil properties at locations without CPTu tests cannot be estimated at various depths with high confidence. This motivates a methodology to clearly identify the soil strata and reduce the uncertainties in prediction of design properties, paving the way for a more cost-effective geotechnical design.

Following the introduction, the structure of the thesis is given as below. • Chapter 2 presents a review of the methods proposed in the literature for estimation of the soil type behavior from in-situ test results. It also gives a short introduction on different techniques available in the literature to estimate the correlation structure of the field. • Chapter 3 describes the scope of the thesis and introduces the aspects in the project overview. • Chapter 4 gives a summary of the included international conference and journal papers. • Chapter 5 concludes the thesis with a summary and discussion of the methodology and assumptions employed in the thesis. Furthermore, the main results and recommendations for future studies are presented. • Appendix A contains the enclosed conference paper titled “CPTu-based geotechnical site assessment for offshore wind turbines—a case study from the Aarhus site in Denmark”. • Appendix B contains the enclosed conference paper titled “Geotechnical site assessment by Seismic Piezocone Test in the North of Denmark”. • Appendix C contains the enclosed conference paper titled “Estimation of soil type behavior based on shear wave velocity and normalized cone data in the north of Denmark”. • Appendix D contains the enclosed journal paper titled “Spatial correlation length of normalized cone data in sand: A case study in the North of Denmark”. • Appendix E contains the enclosed journal paper titled “Effect of spatial correlation length on the interpretation of normalized CPT data using a Kriging approach”.

The field of offshore wind energy is engaged with many problems and different methodologies within civil and geotechnical engineering. Many challenges are related to the estimation of the soil properties within a site for the purpose of design and analysis of the foundations. In recent decades, there has been a shift in favor of utilizing in-situ testing methods for subsurface investigation and evaluating the engineering soil parameters as an alternative to the conventional laboratory testing; but still the identification of soil stratification at locations with no direct measurement is accompanied with many uncertainties due to variability of soil. In this chapter, a brief discussion of different methods in the field of site investigations is presented. Also different methodologies to estimate soil parameters from field measurements are reviewed. This chapter also presents different methodologies for estimation of soil variation presented in the literature.

Soil stratification is essential in geotechnical site characterization and structural design (Houlsby and Houlsby, 2013; Wang et al., 2014). Recent studies have reported the significant effect of soil stratification on the design of foundations, tunneling, and pipelines (Burd and Frydman, 1997; Padrón et al., 2008; Huang and Griffiths, 2010; Zhang et al., 2012; Lee et al., 2013; White et al., 2014). The identification of soil stratification includes determining soil types, the number of soil layers, the thickness of each layer and soil properties. The standardized cone penetration test (CPT) and piezocone (CPTU) have been widely used to infer the soil type by directly interpreting measured CPT/CPTU parameters (e.g. Schmertmann, 1978; Douglas and Olsen, 1981; Robertson and Campanella, 1983; Robertson, 1990; Jefferies and Davies, 1993; Olsen and Mitchell, 1995; Eslami and Fellenius, 1997; Lunne et al., 1997; Schneider et al., 2008). Several classification charts were proposed in the literature to classify the subsurface soil from the CPT data. These charts were developed based on comparison/correlation between CPT/PCPT data profiles and soil type data bases collected and evaluated from extensive soil borings. The first soil classification chart based on cone resistance (qc) and sleeve friction ( fs ) was pioneered by Begemann (1965). Douglas and Olsen (1981) employed the electrical cone penetrometer in their soil profiling chart, including trends for liquidity index and earth pressure coefficient, as well as sensitive soils and “metastable sands”. Jones and Rust (1982) proposed a chart based on the piezocone using the measured total cone resistance and the measured excess pore water pressure mobilized during cone advancement. Due to increasing parameters like cone resistance and friction ratio with depth, the chart has the deficiency of classifying soil in a different group but it is interesting because it identifies the consistency of fine-grained soils and the density (compactness condition) of coarse-grained soils. Robertson et al. (1986) and Campanella and Robertson (1988) were the first that corrected cone resistance for pore pressure at the shoulder [ qt = qc + u (1 – a)], where qt is the cone resistance corrected for pore water pressure on shoulder, qc is the measured cone resistance, u2 is the pore pressure measured at cone shoulder, a is the ratio between shoulder area (cone base) unaffected by the pore water pressure to total shoulder area. As a refinement of the Robertson et al. (1986) method, Robertson (1990) considered the normalization for overburden stress in the profiling chart to compensate for the cone resistance dependency on the overburden stress. Zhang and Tumay (1996) performed some investigations on overlaps of different soil types due to uncertainty in CPT classification systems. Their work was based on the statistical and fuzzy subset approaches. Eslami and Fellenius (2004) developed a new method for soil profiling by plotting effective cone resistance (qE ) versus sleeve friction with a compiled database from 20 sites in 5 countries. Based on data from the corrected tip resistance ( qt ) and penetration pore-water pressure at the shoulder (u2), Ramsey (2002) evolved a model for classifying soil with a simple criterion. Based on this conservative criterion, whenever the charts predict different zones, then the zone with the lower numerical value should be chosen. The soil classification charts proposed by Schneider (2008) were based on normalized piezocone parameters using parametric studies of analytical solutions, field data, and judgment based on the previous discussions. The three models proposed in the method are exactly the same but have been plotted in different formats. The soil types, essentially drained sand and transitional soils, can also be described in these models. Using probabilistic methodology, considering the inherent uncertainties, Cetin and Ozan (2009) proposed a cone penetration test (CPT) soil classification. The resulting database was probabilistically assessed through Bayesian updating methodology allowing full and consistent representation of relevant uncertainties, including model imperfection, statistical uncertainty and inherent variability.

CPT measurements should be normalized for vertical stress because it has a significant influence on CPT data and lead to an incorrect assessment of soil strength parameters. Studies show that if overburden stress effects are not properly taken into account, raw cone penetration test (CPT) measurements can be misleading. Low overburden stresses, found at shallow soil depths, will result in a small measured tip and sleeve resistance, whereas large resistances are generally encountered at greater soil depths. According to Moss et al. (2006), a logarithmic increase is recorded with depth in homogeneous soils. The bulk of the research on CPT normalization was conducted to account for the effects of overburden stress. Robertson and Wride (1998) proposed the following technique for normalizing cone tip resistance measurements: where qc1N is the dimensionless cone resistance normalized due to the weight of soil on top of the cone, qc is the measured cone tip resistance, and CQ is a correction factor for overburden stress. The exponent n takes the values 0.5, 1.0 and 0.7 for cohesionless, cohesive and intermediate soils respectively, whereas σ'ν0 is the effective vertical stress and Pa is the reference pressure (atmospheric pressure) in the same units as σ'ν0 and qc, respectively. Also, the normalized friction ratio is calculated using the equation proposed by Wroth (1984): where fs is the measured sleeve friction and σν0 is the total vertical stress. The values of qc ,σν0 and fs are all in the same units.

The seismic piezocone penetration test (SCPTu), as a novel development of CPTu, provides shear wave velocity ( Vs ) measurements during the sounding and provides more direct information in estimation of geotechnical parameters like deriving small strain shear modulus (Lunne et al., 1997; Mayne and Campanella, 2005; Liu et al., 2008; Cai et al., 2009). In the absence of direct shear wave velocity measurements, many empirical correlations have been proposed between shear wave velocity and measured cone resistance and sleeve friction (e.g. Baldi et al., 1986; Mayne and Rix, 1995; Hegazy and Mayne, 1995; Mayne, 2006). Also the low-strain shear modulus (Gmax or G0) can be found using the shear wave velocity measurements obtained by assessment of SCPTu, since elasticity theory relates the shear modulus, soil density (ρ) and the shear wave velocity as Gmax = ρVs². To obtain the low-strain shear modulus, a sm all rugged velocity seismometer has been incorporated into the cone penetrometer (Robertson et al., 1986). Figure 2-1 illustrates a schematic layout of the standard downhole technique. A suitable seismic signal source should generate large amplitude shear waves with little or no c ompressional wave component. Usually an excellent seismic shear wave source consists of a rigid beam, steel jacketed and weighted to the ground. Many correlations for determining Gmax based on cone resistance have been recommended for a large variety of soils, either granular (Baldi et al., 1989) or cohesive (Mayne and Rix, 1993) or both soils (Hegazy and Mayne, 1995). As examples, Rix and Stokoe (1992) proposed a correlation for sands and Mayne and Rix (1993) showed that for a wide range of clays the small strain shear modulus is a function of in situ void ratio (e0) and cone resistance ( qt ) (Cai, 2010). Figure 2-1 Robertson et al. (1995) proposed a soil classification chart based on normalized cone resistance ( Qt ) and the ratio of small strain shear modulus ( G0 ) to cone resistance ( G0 / qt ), and a variety of soils such as highly compressive sands, cemented and aged soils and clays with either a high or low void ratio can be identified through the chart (Lunne et al. 1997). It should be noted that all classification charts are global in nature and provide only a guide to soil behaviour type.

Knowledge about the soil variability in the design and analysis of foundations is a key factor in verification of new design codes and therefore is of great interest in geotechnical engineering. Limited available information results in more conservative geotechnical designs (e.g. Baecher, 1986). As examples, Alonso and Krizek (1975), Tang (1979), Nadim (1986), Campanella et al. (1987), Wu et al. (1987), Reyna and Chameau (1991), Kulhawy t al. (1992), Fenton (1999), Phoon et al. (2003) and Elkateb et al. (2003a, 2003b) have performed some study to assess the inherent variability of soil using cone penetration tests (CPT). But only a few numbers have used stress-normalized CPT data (Uzielli, 2005). Fenton and Vanmarcke (1990) proposed the local average subdivision (LAS) method for modeling the inherent variability of a soil property as a random field. The method requires probability density functions (pdf). Input parameters are described by the mean p and standard deviation o of the property at each point in space, and a spatial correlation length δ. Vanmarcke (1977) reported spatial correlation functions and spatial correlation lengths using common functions such as exponential, exponential oscillatory, quadratic exponential oscillatory and bilinear. In geotechnical investigations, developing new ways to determine soil properties using statistical approaches are important. Probabilistic methods have been proposed in geotechnical engineering for estimating uncertainties in geotechnical predictions (e.g. Zhang et al., 2011), and the application of geostatistics to large geotechnical projects has been approved as a powerful tool in analysis and design (e.g. Ryti, 1993; Rautman and Cromer, 1994; Wild and Rouhani, 1995; Rouhani, 1996). The Kriging method, based on D. G. Krige's empirical work for assessing mineral resources (Krige, 1951), and later formulated by Matheron (1962) into a statistical approach in geostatistics can be used to stablish a spatial interpolation between known data. Kriging generates a best, linear unbiased estimate of a random field between known data by having the ability of estimating the mean trend (see e.g. Fenton and Griffiths, 2008). In environmental and geotechnical engineering, Kriging is commonly applied to the mapping of soil parameters and piezometric surfaces (e.g. Journel and Huijbegts, 1978; Delhomme, 1978; ASCE, 1990).

A realization of the soil variability for the purpose of analysis and design of foundation is a basis for calibration of new design codes. Due to limited site data and natural variability of soil parameters, foundation design is usually accompanied with significant uncertainty. In the case of limited available information, geotechnical design is inevitably more conservative, cf. e.g. (Baecher, 1986). Similar to the mean and standard deviation of soil parameters, the spatial correlation length has a great influence on determining the probabilistic outcomes.

The identity of the soil type can only be obtained at the location at which a CPT is conducted. If the soil type at nearby locations is required during a design or construction process, the results at the existing location generally cannot be used directly due to the significant variability of natural soils (Lloret-Cabolt et al., 2014). The stratification of natural soil may change greatly within a small horizontal distance of say 5 m (Das, 2010). The evaluation of soil stratification at unsampled locations with no available data remains an unsolved problem. The interpolation technique can give a rough estimation of a certain soil parameter at unsampled locations based on existing CPT data (Beacher and Christian, 2003; Lacasse and Nadim, 1996). This estimation will inevitably vary in a wide range due to the considerable variability of CPT measurements as well as the uncertainties associated with soil classification methods (e.g. Zhang and Tumay, 1999; Kurup and Griffin, 2006; Jung et al., 2008; Cetin and Ozan, 2009; Wang et al., 2013). Therefore, clear determination of soil stratification from a scattered and obscured estimation of soil parameters is difficult (Houlsby and Houlsby, 2013). If statistical characteristics of soil properties are independent from spatial location, they are called statistically homogeneous. The first step to characterize the inherent spatial variability of soil properties is to identify statistically homogeneous sub-layers with the same characteristics by interpreting the available data. When the results of soil classifications performed on samples retrieved from bore-holes are available, identifying layers with similar soil types is straightforward. For in situ tests such as the cone penetration test (CPT) where no specimens are obtained, the identification of layers with the same soil type must be based on indirect methods as explained in detail in previous sections.

Depicting of how rapidly the field varies in space enables us to characterize a random field. This is achieved by the second moment of the field's joint distribution, which is defined as the covariance function, where μx(t) is the mean of X at the position t. A more meaningful measure about the degree of linear dependence between X(t') and X(t*) is the correlation function, where σX(t) is the standard deviation of X at the position t. A commonly applied model of the correlation function in geostatistics is a single exponential curve, proposed by a great number of related research and mathematical simplicity, cf. e.g. (DeGroot, 1996; DNV, 2010).

The spatial correlation length, also known as the scale of fluctuation, is the distance for which points are highly correlated and reflects the variability of a strongly correlated domain. The correlation length for a one dimensional real valued field is defined as the area under the correlation function (Vanmarcke, 1984): There are different techniques available in the literature for the estimation of the spatial correlation length. Vanmarcke (1977) approximated correlation functions and the scales of fluctuation of residuals by use of such common models in Table 1. For example, DeGroot and Baecher (1993) employed the exponential model to estimate the horizontal scale of fluctuation of undrained shear strength in a soft marine clay layer as 46 m and using the squared exponential model, Tang (1979) estimated the horizontal scale of fluctuation of cone resistance of CPT data in a marine clay layer as 60 m. Several common admissible models for correlation functions proposed within the geotechnical and geohydrological literature are presented in Table 2-1. Most studies in geotechnical site investigations illustrate higher correlation length in the horizontal direction rather than vertical due to the horizontal formation of soil strata, in which soil properties are more correlated. As an example and from the reported experimental data in literature (JCSS-C1. 2006), the horizontal correlation length for the tip resistance in sea clay is around 40 m, whereas it is 2 m in vertical direction (Chiasson and Wang, 2006). Table 2-1. Autocorrelation models and the corresponding spatial correlation length (after Vanmarcke, 1977) (JCSS probabilistic model code)

Since its introduction in the 1960s, Kriging has been widely applied to many areas of engineering and science, including geostatistics. In environmental and geotechnical engineering, Kriging is commonly applied to the mapping of soil parameters and piezometric surfaces (e.g. Journel and Huijbegts, 1978; Delhomme, 1978; ASCE, 1990). Principally Kriging is a best, linear unbiased estimation with the added capability to estimate the mean trend. The main application of Kriging is to provide a best estimate of the random field at unsampled locations and is modelled as a weighted linear combination of the observations. Assume that X1 , X2, ..., Xk are observations of the random field X(x) at the points x1, x2, . . , xk, that is, Xk = X(xk). A Kriging estimator is said to be linear because the predicted value X is a linear combination that is written as: where the n unknown weights βk are solutions of a system of linear equations which is obtained by assuming that X is a sample-path of a random process X. The hat in X shows that it is an estimation. Naturally, when the point Xj is close to one of the observation points, the corresponding weight βj should be high. In contrary, when the random field X(x) and Xj are in different (uncorrelated) soil layers, probably βj is small. The error of prediction of the method is to be minimized. The Kriging assumption is that the mean and the covariance of X is known and then, the Kriging predictor is the one that minimizes the variance of the prediction error. Kriging has some merit compared to other common interpolation techniques. For example, it can generate site-specific interpolation layout by directly integrating a model of the spatial variability of the data (Rouhani, 1996). Stochastic dependency in geotechnics can be due to the geological processes acted over a large domains across geological period (e.g. sedimentation in large basins) or in fairly small areas for only a short time (e.g. turbiditic sedimentation, glacio-fluviatile sedimentation).

Modelling of the soil as a random field requires a numerical stochastic analysis. The first step in such analysis is performing a random field simulation. Different methods proposed in geotechnical practices to generate multidimensional random fields. The most common algorithms are: Correlation Matrix Decomposition or Cholesky decomposition method. Turning Bands Method (TBM). Moving Average (MA) methods. Fast Fourier Transform (FFT) method. Local Average Subdivision (LAS) method. Discrete Fourier Transform (DFT) method. All methods use the same procedure by generating a set of spatially correlated random field from a set of uncorrelated standard Gaussian (zero mean and unit standard deviation) distributed random seeds. The correlation is introduced via a correlation function. Transforming from the Gaussian distributed field to the desired field (e.g. log-normally distributed) with the specified mean and standard deviation is carried out afterwards. The correlation matrix decomposition method is the direct method of generating random field with the specified correlation matrix (Fraleigh and Beauregard, 1990). Turning bands method was originally proposed by (Matheron, 1973) for second-order stationary fields and is a fast method when dealing with a big two- or three-dimensional random field. The correlation matrix decomposition method was used in the verification part of this study due to simplicity and speed of generation.

In correlation matrix decomposition method, the random field is generated directly using a specified correlation function for the field, ρ. If ρ is a positive definite matrix, then a factorization of ρ can be produced as Eq. (7) (Fraleigh and Beauregard, 1990): where L is a lower triangular matrix. Eq. (8) is typically solved using Cholesky decomposition and matrix L is used for correlating a set of uncorrelated standard Gaussian random seeds. Below, steps for generating a random field using matrix decomposition method are given. Generate a set (vector) of standard Gaussian distributed seeds, Unx1, where n is the number of samples or locations, Construct the correlation matrix, ρnxn, using the specified correlation function for the field, Decompose the correlation matrix by solving Eq. (8) and find the lower triangular matrix, Lnxn, Multiply matrix Lnxn to vector Unx1 inorder to generate a vector of correlated random samples, Ynx1 as Ynx1 = LnxnUnx1, Transfer the correlated random field, Ynx1, to the field Xnx1 having considered the cumulative distribution function (CDF), F : where xj and yj are the ith entry of Xnx1 and Ynx1, respectively. Further, Φ(.) is the standard Gaussian CDF. As an example, a two-dimensional (2D) random field for the cone resistance of soil is shown in Figure 2-2. Figure 2-2

As mentioned in the previous chapter, several empirical correlations have been proposed in the literature for estimating the soil behavior type and strength parameters from in-site testing methods. Nevertheless, compatibility of these methods should be considered in a local case. Also due to inherent variability of the soil layers, those estimations are accompanied with many uncertainties and should be taken into consideration. This chapter explains the overall aim of the current PhD thesis. Also the main objectives of the project as well as its novelty are pointed out.

Site characterization is a unique problem in geotechnical engineering that utilizes both prior information (including engineering judgment) and project-specific information from test borings, in-situ testing, and/or laboratory testing. The problem is further complicated by inherent spatial variability of geo-materials and the fact that only a small portion of geo-materials are examined during site characterization. Some research is conducted about reliability based design of wind turbine foundations. However, limited research has been carried out regarding the spatial co-variation of soil parameters over a large field. The conventional method for determining a so il type is by laboratory classification of samples retrieved from a borehole. If a continuous, or nearly continuous, subsurface profile is desired, the cone penetration test (CPT) provides time and cost savings over traditional methods of sampling and testing. CPT results are typically used to infer soil types and soil properties. Specifically, CPT are used for determining soil classification, obtaining the drained and undrained shear strength parameters of sand and clay deposits, and estimating the deformation modulus for designs of geotechnical structures. The aim of the project is to formulate a method for probabilistic site description based on cone penetration tests and establish a probabilistic method that enables a reliable foundation design for offshore wind farms, which requires fewer tests than present methods.

Considering the aspects introduced in the project overview, the objectives of the present study can be categorized as following: Conducting several cone penetration tests in different sites and estimating the soil type of the region using various soil classification charts by considering an inherent uncertainty for the model and method-verification using laboratory classification test results on samples retrieved from bore-holes. The sites chosen for analysis, even if they are on land, are representative for the soil conditions that can be expected in an offshore wind farm. Comparing the results for the purpose of choosing the best method compatible with the soil type of the region as a case study. This help engineers to find the best compatible classification method for the soil in high cost projects (e.g. site investigation phase for the offshore wind turbine foundation analysis). Performing several seismic cone penetration tests in both sand and clay and analyzing data based on different correlations presented in the literature to estimate shear wave velocity and shear moduli of the soil based on cone data. Two seismic analysis methods are employed to estimate the shear wave velocities from time acceleration data to see which one is more reliable in estimation of shear wave velocity. The results are further compared and verified with the measurements of shear wave velocity achieved from SCPTu tests. The seismic tests are carried out because the elastic properties of the soil must be found with high accuracy since the serviceability limit state has been found to be the design driver in many cases. Such studies decrease the uncertainty regarding the choosing method for estimation of soil parameters in analysis of offshore wind turbine foundations. Shear wave velocity measurements obtained from SCPTu tests are used in the classification chart based on small strain shear modulus and normalized cone resistance. The results are further compared and verified with the classification test results of samples retrieved from boreholes on the site. Performing a reliable estimation of soil properties of the field, as well as the knowledge about variation of soil parameters and soil inhomogeneties in both vertical and horizontal direction. The main topic of this part is spatial analysis of the measurements from the CPTu tests performed in the field. This study seeks to estimate anisotropic spatial correlation length of two sandy sites in northern Denmark, using statistical trends and correlations, and to interpolate soil properties at unsampled locations of cone data. Creating random field models to deal with uncertainty in soil properties due to the spatial variability. This is achieved by analysing some in-situ cone penetration test (CPT) data from a sandy site in the region. In order to provide a best estimate of properties between observation points in the random field, a Kriging interpolation approach has been applied to interpolate between known borehole data. Studies such as this can reduce the cost of site investigation by providing more reliable interpolated information for design and analysis of offshore wind turbine foundations.

The current PhD thesis has been divided into three research parts and concluded in 5 scientific papers, cf. Figure 3-1. Part I focusses on the estimation of soil stratigraphy using CPT in-situ testing method and classification methods. Part II presents interpretation of seismic cone penetration tests in sand and clay and its application to estimate the shear moduli of the soil using seismic analysis. Also estimation of the soil type by having the values of small strain shear modulus is presented in this section. Figure 3-1 Part III concerns the modelling of spatial variability at the site by introducing the spatial correlation length of cone data. Also this part presents a probabilistic method to predict cone data at unsampled locations by realization of a random field and applying the Kriging estimation method.

The current PhD project is disseminated via five scientific papers, including three conference paper and two journal papers which can be found in the enclosed appendices. The papers come along with the objectives of the research project during the PhD program. In the following chapter, the significant outcome of the papers is given including assumptions, methodology and results.

Published in Twenty-second International Offshore and Polar Engineering Conference, Rhodes, Greece, pp. 151-158. The paper title is “CPTu-based geotechnical site assessment for offshore wind turbines—a case study from the Aarhus site in Denmark”. This study presents a thorough site investigation of a wind farm at Aarhus, using different CPTu-based soil classification methods. These include methods by Robertson et al., (1986), Robertson (1990), Ramsey (2002), Eslami and Fellenius (2004) and Schneider (2008). The data from 41 CPTu tests and five bore-hole tests have been used. The raw cone penetration measurements are scrutinized and removed further for data connected with physical or mechanical errors. The corrected data were then used for classifying soil by the above mentioned charts and uncertainties related to each method estimated by presenting a model preference to show how certain the method is about the soil type of each data point. For this purpose, the classification diagram is digitalized (in this case a resolution of about 2000 × 2000 pixels is used) and a window is defined around a given data point. The size of the window is a heuristic choice meaning that a larger window implies more candidates for the soil type proposed by the classification method. Main results The main findings from Paper 1 are: Even though the cone penetration test is a standard method of assessing soil properties, errors related to measuring can still occur during the test. Here measurements with considerable peaks are removed. These peaks are basically due to stiff thinly interbedded materials within the soil deposits and are not representative of the soil type in that location. This is basically based on engineering judgment, and is very important as this removal has effects on the classification results. In Figure 4-1, an example of this error filtering is illustrated for a representative borehole by red circles marking the suspected measurement. All CPT classification methods are based on the idea that combinations of CPT parameters falling within a “zone” in the classification chart are classified as a particular soil type. However, the lines separating the “zones” are not resulting from theoretical solutions and subject to uncertainty in the sense that the engineer has to decide whether a given data point is in one or another “zone”. The certainty introduced in the soil classification chart is a probability meaning that it is always between 0 and 1.Figure 4-2 shows that for measurements which are close to the borders this value is small (close to 0) and for those which are far from border lines it is close to 1. Figure 4-1 Figure 4-2 Figure 4-3 The results from comparison with bore-hole data showed that most of CPT classification methods, in general, are acceptable for classifying the soil, but some of them are more confident with higher certainties in some specific soils. This emphasizes that different methods have different capabilities in identifying correctly various soil behavior. This is possibly related to the differences in the development processes behind the charts, due to different background data. The comparisons between different classification methods and verifications with bore-hole results provide guidance for soil of the region to be assessed in the future with fewer tests, which results in saving time and expenses. Discussion and concluding remarks Error filtering is an initial and important part of the evaluation of CPT data. Main errors are due to either local soil inhomogeneity or big halts during the sounding. Peaks occur when the cone reaches a thin layer of stiff material such as lenses of stiff silt or sand or small stones or boulders within the layer. These peaks should be carefully removed as they lead to a considerable error in predicting the real parameters of the entire layer. The errors due to halts often happen when a new rod should be attached to reach further depth. These errors appear as large drops in the cone resistance and big change in drained conditions. The size of the window for estimating the soil type reflects the uncertainty related to a visual interpretation of the printed diagram. A smaller window implies that the soil types assigned to measurements near zone boundaries are classified with more confidence. In future analysis basis on visual interpretation of the diagram, it is advised to employ different size of the windows and perform a sensitivity analysis to find the best size for the window.

Published in Seventh International Conference on Case Histories in Geotechnical Engineering, Wheeling, IL. Missouri University of Science and Technology, 2013. Paper no. 2.34. The paper title is “Geotechnical site assessment by seismic piezocone test in the north of Denmark”. There are different correlation methods reported to predict shear modulus from CPTu data, but their validity still needs to be verified for a local case. So the paper presents a description of performed SCPTu and shear wave types in both sand and clay as a case study along with two different methods of finding S-wave velocities in order to analyse and compare with the values obtained from empirical correlations presented in the literature. The measurements of shear wave velocity achieved from SCPTu tests are further compared and verified with the results. Main results The main findings from Paper 2 are: Several seismic cone penetration tests were performed in two sites (one with mostly clayey soil and the other with mostly sand) in the north of Denmark with generating two pulses on the ground surface (Figure 4.4). All SCPT readings were taken with intervals of 1 m. Two analysis methods, “Reverse polarity” and “Cross-correlation”, were employed to calculate shear wave velocities from signal traces of seismic data, and the results were compared to each other to investigate which method is more compatible in the region. Figure 4-5 illustrates an example of time series in each analysis method. Since only one strike (left or right) is enough in the cross-correlation method to estimate the shear wave velocity, the interval time that sounding is halted is shorter compare to the reverse polarity method in which two strikes are needed. This can be counted as a disadvantage of the reverse polarity method. Also the point at which two strikes are superimposed should be chosen by the analyst, which increases the uncertainty of the procedure. Because by introducing a different cross-point, the value of shear wave velocity changes while in cross correlation method the shear wave velocity is estimated by mathematical analysis. The Cross-correlation method removes human bias and gives realistic error estimates. Figure 4-4 Figure 4-5 Comparison of the shear moduli calculated from CPTu data using empirical correlations with the SCPTu field test results show that the empirical methods over estimated the modulus. This is shown in Figure 4-6 by comparing shear modulus values obtained by empirical methods and from field data. Figure 4-6 Discussion and concluding remarks Even though the seismic cone penetration test has some merits, many considerations should be taken into account during the manipulation and data analysis. As shown in Figure 4-7, the difference between field tests and empirical methods is considerable. Many factors could be involved in the final results of the study. The first and the most possible factor is the existence of the background noise in the area. This noise is visible from the first and/or last part of the signal, before/after the passage of the wave produced by the hammer. Vibrations from sources such as traffic can disturb the main signal produced by the hammer, leading to erroneous predictions of the wave speed In addition, when the tests are carried out at depths with a difference of one meter, the velocities are not directly representative for the soil deposits that are determined based on the standard CPT assessment and borehole logging. Instead, the velocities are mean values for the 1 m deep layers present between adjacent measurement positions. The big difference between three analysis methods in the field test diagrams could be due to not providing similar conditions to produce the left and right strike. Also the important effect of choosing the intersection point in reverse polarity analysis method should not be ignored (Fig. 4-8). Figure 4-7 As a h istorical note, the reverse polarity method was invented in a t ime when the recorded signals were analogue. Today the recordings are digital so that users have much more stronger capabilities to do something more significant than pick of a single point where two wavelets are superimposed. Figure 4-8 Figure 4-8 shows an example of wrong analysis based on two strikes. In such cases that the results are too sensitive and the reversal signals are overall not good, it might be recommended to use a first arrival (or first peak) method or cross-correlation analysis based on only one-direction single signal (Campanella 1986). In the paper published in 7ICCHGE, shear velocities obtained from empirical correlations are plotted for each 2 cm in Fig. 10. However, it can be argued that this is subject to come uncertainty because these values are based on relative densities estimated from CPT measurements. In future analysis, it is advised to find densities from intact samples at the site and compare with the results.

Published in 3rd International Symposium on Cone Penetration Testing, Las Vegas, Nevada, USA. Pp. 621-628. The paper title is “Estimation of soil type behaviour based on shear wave velocity and normalized cone data in the north of Denmark”. In this paper, the chart by Robertson et al. 1995 b ased on s mall strain shear modulus and normalized cone resistance was employed to classify the soil using SCPTu data from a sandy site. Using two different analysis methods, the values of shear wave velocity and subsequently small strain shear modulus have been obtained and applied in the chart to estimate the soil type of the region. The results are further verified and compared with the soil classification test results on the samples retrieved from boreholes. Main results The main findings from Paper 3 are: After correction of measured data from the CPT and normalizing the cone resistance for the effect of overburden pressure, the data were used in the chart proposed by Robertson et al. (1995) based on shear wave velocity measurements. Results are illustrated in Figures 4-7 and 4-8 for a representative SCPTu sounding profile. Figure 4-7 Figure 4-8 Elasticity theory relates the shear modulus, soil density (ρ) and the shear wave velocity (Vs) as Gmax=ρV2. Therefore, by performing seismic cone penetration test in the region, the values of small strain shear moduli needed in the Robertson chart could be obtained. The analysis of measurements from all of the soundings reveal that the chart proposed by Robertson et al. (1995) is well-predictive at this site, and in the lack of information due to limited soil samples it seems reliable to use the results of SCPTu to predict the soil type. Discussion and concluding remarks SCPT analysis has been performed using two different methods: Cross-correlation and Reverse polarity. Both methods have some merits in calculating the velocity but need some consideration to avoid any misinterpretation. In reverse polarity method two strikes are needed; hence the need for a clear reversal signal may arise. However, it can be argued that this is subject to come uncertainty in the absent of such clear signals. It is advised to use cross-correlation method for data analysis in such cases. As shown in Figure 6 in the paper, there are some white lines in the certainty diagram. The meaning for these layers is that cone parameters corresponding to these depths fall beyond of the classification chart and no zone could be assigned to them. So the method cannot predict any soil type to these measurements. In the case that these layers are presented many times, reconsideration in the method for soil classification is needed. Also the measurement uncertainty could be a possible reason for these incompatibilities in the diagram.

Published in Canadian Geotechnical Journal, Vol. 51, No. 8, pp. 844-857. The paper title is “Spatial correlation length of normalized cone data in sand: A case study in the north of Denmark”. The paper focuses on the spatial variability of cone data normalized with respect to vertical stress. The data were collected at two different sites in the north of Denmark. To characterize a random field, the knowledge about how rapidly the field varies in space is needed. This is captured by the covariance structure of the data. By calculating the statistical parameters of the cone data, the spatial correlation length of the field was estimated in the vertical and horizontal directions. At both sites, the cone data show that the vertical and horizontal correlation structures in soil properties are strongly anisotropic, with shorter correlation lengths in the vertical direction. Main results The main findings from Paper 4 are: The coefficient of variation, COV, is a d imensionless value that quantifies the relative deviation between individual data sets with different means. It is generally more useful than the standard deviation for the comparison of one raw data set with another raw data set. Since COV is an indicator of the degree of variation in soil properties across the site, in soil layers with relatively high COVs, there is expectation for more variability of the soil parameters. In the horizontal direction, the maximum COVs occurred in the last layer of sand deposits in the Frederikshavn site. This effect may be due to thinly interbedded silt mixtures within the layer. A random field is described concisely in the second moment sense by estimating the spatial correlation length and the coefficient of variation in space. For this purpose, the average coefficient of variation of cone data in vertical and horizontal directions was calculated in two sites, and regression analysis was employed to estimate the spatial correlation length. Characterizing the spatial variability of soil properties shows that due to the geological nature of deposits and the material composition of the formations, the vertical and horizontal correlation structures from the cone results are significantly anisotropic, with higher values in the horizontal direction (Figures 4-9 to 4-11). Inclination of soil layers has a significant effect on the obtained values of horizontal correlation length. Under the simplifying assumptions that the soil layers are ideally horizontal and homogenous, the measured parameters at the same depth must be highly correlated with the same measured values. Though in reality, due to the inclined layer within the soil deposit, it is more likely for soil parameters to have different values at the same depth and this result in a poor correlation. Figure 4-9 Figure 4-10 Figure 4-11 Discussion and concluding remarks Since effective overburden stress has a considerable influence on the soil interpretation, CPT measurements have been normalized for vertical stress. To have a certain comparison between two different sites, and avoid the influence of the depth on the results, data normalization proposed by Robertson and Wirde (1998) was used in this study. It should be noted that the Robertson classification method also employs normalized cone data (Qt and FR) to estimate the soil type. Therefore, qc1N and Qt should not be mixed up in the conclusion. The observed variations of the vertical correlation length in FR and qc1N imply weaker correlation structure in friction sleeve measurements. A friction sleeve with a length of 133 mm includes 6 consecutive friction readings per each 2 cm penetration. This means that the instrument in itself is correlating the data because each measurement is contributing in the procedure several times. Hence, one could argue that correlation lengths shorter than about 200 mm can hardly be achieved. Such correlation lengths would be expected alone due to the inherent smoothing provided by the sleeve and the process of taking a running average. Therefore, the small correlation length obtained in the vertical direction clearly indicates low correlation over depth.

Published in Journal of Geotechnical and Geoenvironmental Engineering (ASCE). Vol. 141, No. 12, 04015052. The paper title is “Effect of spatial correlation length on the interpretation of normalized CPT data using a Kriging approach”. The article presents a Kriging approach applied to the normalized cone resistance of a sandy site in Denmark to interpolate between known borehole data. By generating a 3-D standard Gaussian random field and sampling some values at discrete (”bore-hole”) locations, Kriging was used to interpolate between the discrete values and compared with the original random field. By calculating the difference between Kriging estimation and generated random field, known values of the cone data at the location of the sounding were taken as observation points to estimate the values of cone resistance at any point within the field. Main results The main findings from Paper 5 are: The correlation length has an inevitable effect on the interpolated values in a way that by increasing the correlation length, more accurate estimates could be obtained at a greater distance. Verification of the method using a random field simulation and the small mean value of the error shows that Kriging interpolation approach and assumptions employed in the method are admissible. Applying Kriging to real values of cone data help us to analyse the effect of correlation length on the results in both vertical and horizontal directions. The results indicate that when the horizontal correlation length increases, the standard deviation of estimated values by the Kriging method decreases, resulting in less uncertainty in prediction of values at intermediate locations. Excellent agreement between the predicted values of normalized cone data and the existing test data (at the location of soundings) emphasizes that correlation structure of the field in a s tatistically homogenous layer is chosen properly. Discussion and concluding remarks Even though Kriging is a preferred method for data interpolation, many considerations should take into account to avoid any misinterpretation. Kriging uses a weighting which assigns more influence to the nearest data points in the estimation of values at unknown locations. To calculate the estimate, Kriging depends on s patial and statistical relationships so it is essential to be aware of correlation structure of the data. If a weak correlation is ruling, then estimated points are only an average of the dataset. An example is a field with small spatial correlation length. The Kriging has a two-step process of semi-variance estimations and performing the interpolation. Some advantages of this method are the incorporation of variable interdependence and the available error estimator output. A disadvantage is that it requires more input from the user and substantially more computing and modelling time. Kriging belongs to the family of linear least squares estimation algorithms. The estimator error is the difference between estimated and real but unknown values and is the error of prediction. The Kriging predictor is the one that minimizes the variance of the prediction error. In a case study, it is important to be aware of this estimation error to have a better interpretation of the result.

The current PhD thesis conveys a comprehensive study on a statistical approach to integrate prior information and project specific test results for probabilistic characterization of soil properties from a limited number of tests. For this, being able to make a consistent classification of soil type and strength parameters at a given site is crucial and this leads to a repeatable and highly standardized method by using cone penetration test due to the large amount of information collected continuously throughout a soil deposit. By focusing on the spatial variability of cone data normalized with respect to vertical stress, the spatial correlation length of the field was estimated in the vertical and horizontal directions to be used in the Kriging interpolation approach to provide a map of normalized cone resistance at the site.

Due to economy, simplicity, continuity, accuracy and efficiency features, cone penetration tests have been turned into an alternative to conventional laboratory testing. One of the most important applications of CPT is in soil stratigraphy and classification profiling. The results can be used further in estimation of shear strength parameters of soils and deformation moduli for the purpose of design and analysis of foundations. Different methods exist for soil profile interpretation from CPT data but their validity still needs to be verified since the original soils used in the chart development are quite different from a local soil. This study attempts to do m ore investigation on different CPTu-based soil classification method adequacies to have a better assessment of the region soil type. This was done by intact sampling and doing some usual classification laboratory tests and comparison with method predictions. These include methods by Robertson et al. (1986), Robertson (1990), Ramsey (2002), Eslami and Fellenius (2004) and Schneider (2008). The results showed an acceptable reliability in most of the CPT classification methods for estimating the soil type. However some of the methods are much more acceptable with higher certainties in some particular soil types compared to others. This can be the result of differences in the development processes of the chart based on different background data. In this specific site, the method by Robertson (1990) based on pore pressure measurements has the highest compatibility with the soil classification test results on samples in sand and gravelly layers, while the Ramsey (2002) models are more reliable in clayey soils. By increasing interest in soil dynamics in the recent years, there is a development of CPT as a seismic piezocone penetration test (SCPTu) with the added ability of taking shear wave velocity measurements simultaneously with measurements of tip resistance (qc), sleeve friction (fs) and pore pressure (u).Different empirical correlations have been proposed between cone data and shear wave velocity measurements to estimate soil parameters but their validity still needs to be verified in a local case and uncertainty remains about the choice of any of these empirical correlations. Two analysis methods from signal traces of seismic data were chosen as “Reverse polarity” and “Cross-correlation”. The field test results of SCPTu and CPTu estimations for shear velocities from empirical correlation are in the same range. Results obtained from empirical methods are conservative compare to the measured values. Also calculations based on correlation proposed by Mayne (2006) results in negative values of shear wave velocities due to small sleeve friction measurements which are not reasonable. So this correlation is not preferred to be used for this region. A number of seismic cone penetration tests have been done in a sandy site in the north of Denmark and results were used to investigate and verify the soil classification system proposed by Robertson et al. (1995). The chart employs the small strain shear modulus and normalized cone resistance to estimate the soil type in the absence of intact soil samples and laboratory test results. The outcomes have been further compared to the soil classification test results on samples retrieved from boreholes in the site. The value of small strain shear modulus is achieved by multiplying the square of the velocity by the density of the soil to be used in the classification chart. The results are very compatible with the laboratory classification results of samples from boreholes by this fact that it is feasible in the future to apply the Robertson et al. (1995) chart to estimate the soil type from SCPT data in this region. This can significantly reduce the cost of site investigation.

Soil variability in CPT test data from two different sites in the north of Denmark has been considered by calculating the COV values of normalized cone data in both directions in homogenous sub-layers identified by the soil classification system proposed by Robertson (1990). In order to characterize the spatial variability of cone resistance and sleeve friction, the autocorrelation function with respect to physical distance has been calculated from measurements of the sand layers. Then by fitting an exponential model to these data, the spatial correlation distance for each variable was estimated. The natural deposition processes of soil causes a significant anisotropy in the vertical and horizontal correlation structures from the cone results, with the vertical length of two to seven times shorter than that in the horizontal direction. Also in the vertical direction, qc1N values are more spatially correlated thanFR, with spatial correlation lengths estimated in the range of 0.5 m and 0.2 m respectively. The same is seen in the horizontal direction. The physical explanation for this is the influences of the soil volume around the cone tip that qc1N measurements are larger than the sampling intervals. Kriging is a w ell-stablished method to predict the values if statistical parameters are available. The purpose was to examine this as a case study. A Kriging interpolation approach has been applied to the normalized cone resistance of the region to provide a best estimate of properties between observation points in the random field. Due to an inevitable effect of correlation length on the map of soil variation by Kriging, a study made to examine the effect of this parameter on estimated values at intermediate locations between known values in the field. This was done for two horizontal correlation lengths in different depths of 2 m and 4 m through the deposit. Results showed that a greater number of intermediate points could be estimated when the correlation length was increased. In contrast these intermediate points could not be estimated precisely by the method when the correlation length was smaller. This means that the estimated points at intermediate locations are close to the mean value of observation points, which implies a higher uncertainty. By increasing the correlation length, the data show more correlation with each other, and the values are closer at a greater distance. A trend in the Kriged qc1N is distinguished and is more obvious by increasing the correlation length. By moving away from the observation point (in a distance larger than correlation length), the method gives an average value of data. Kriging is not a random field generator but a best linear unbiased estimator. It means that by defining a correlation length, the method predicts the values within this distance.

With the inspiration from the conducted studies through the current PhD thesis, the following recommendations are suggested for the future research in this field: Two analysis methods of reverse polarity and cross correlation need to be verified to see which one is more reliable in calculating the shear wave velocity. This can be done by creating a time series with known velocity value and applying both methods to see which one is closer to the desire velocity. Considering the soil layers inclination in calculation may result in a lower value of horizontal correlation length due to reflecting a higher correlation between data. The measured data on the border between two different layers may show more correlation than points which are in the same level but from different soil categories. As a future work, it is important to find these inclined layers in a soil deposit. Studies such as modelling spatial variability of the site using Kriging can be further developed to reduce the cost of site investigation by providing more reliable interpolated information between limited site CPT data.

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IS CITED AS: Firouzianbandpey, S., Ibsen, L. B., Andersen, L. V. (2012). “CPTu-based geotechnical site assessment for offshore wind turbines—a case study from the Aarhus site in Denmark.” Proceedings of the Twenty-second International Offshore and Polar Engineering Conference, Rhodes, Greece, pp. 151-158. STATUS: Published Corrigendum: CPTu-based geotechnical site assessment for offshore wind turbines—a case study from the Aarhus site in Denmark Firouzianbandpey, S., Ibsen, L. B., Andersen, L. V. Ref.: Proceedings of the Twenty-second International Offshore and Polar Engineering Conference, Rhodes, Greece, pp. 151-158 (2012). Figure 5.

IS CITED AS: Firouzianbandpey, S., Nielsen, B. N., Andersen, L. V., Ibsen, L. B. (2013). “Geotechnical site assessment by seismic piezocone test in north of Denmark.” Proceedings of 7th International Conference on Case Stories in Geotechnical Engineering: and Symposium in Honor of Clyde Baker, ed. / Prakash, S.. Missouri University of Science and Technology, Paper No. 2.34. STATUS: Published Corrigendum: Geotechnical site assessment by seismic piezocone test in north of Denmark Firouzianbandpey, S., Nielsen, B. N., Andersen, L. V., Ibsen, L. B. Ref.: Proceedings of 7th International Conference on Case Stories in Geotechnical Engineering: and Symposium in Honor of Clyde Baker, ed. / Prakash, S., Missouri University of Science and Technology, Paper No. 2.34. (2013). Figure 2 is modified to: Figure 2 Figure 3 is modified to: Figure 3 The Caption of Figure 4 is changed to: Figure 4 (a): Sand (Borehole 1) – CPT3 Figure 4 (b): Clay (Borehole 1) – CPT 5 Table 1 Water content results for sand

Borehole 100 is changed to Borehole 1

Borehole 200 is changed to Borehole 2

Table 2 Specific gravity of soil (Sand)

Sample No.	Borehole No.	Sample depth (m)	Specific gravity of soil solid, Gs, [-]	Density, ρ (kg / m3) from laboratory tests on samples
9	1	3.8	2.66	1853
14	1	6.3	2.65	1675
25	3	3.2	2.65	2042
34	3	7.8	2.66	2047

Table 3 Water content results for clay

Sample No.	Borehole No.	Sample depth (m)	Water content (%)
22	1	7.4	34-36
13	1	4.4	36-37

IS CITED AS: Firouzianbandpey, S., Ibsen, L. B., Andersen, L. V. (2014). “Estimation of soil type behavior based on shear wave velocity and normalized cone data in the north of Denmark.” Proceedings of 3rd International Symposium on Cone Penetration Testing, Las Vegas, Nevada, USA, pp. 621-628. STATUS: Published Corrigendum: Estimation of soil type behavior based on shear wave velocity and normalized cone data in the north of Denmark Firouzianbandpey, S., Ibsen, L. B., Andersen, L. V. Ref.: Proceedings of 3rd International Symposium on Cone Penetration Testing, Las Vegas, Nevada, USA, pp. 621-628 (2014). Figure 1 is modified to: Figure 1 The caption of Figure 2 is changed to: Figure 2: Boreholes profile and CPTu results from field test: Borehole 1- CPT 3 Table 1 Water content results for sand

Borehole 100 is changed to Borehole 1

Borehole 200 is changed to Borehole 2

Table 2 Specific gravity of soil results (Sand)

Sample No.	Borehole No.	Sample depth (m)	Specific gravity of soil solid, Gs, [-]	Density, ρ (kg / mm)3
9	1	3.8	2.66	1853
14	1	6.3	2.65	1675
25	3	3.2	2.65	2042
34	3	7.8	2.66	2047

Figure 6 (left): Figure 6

IS CITED AS: Firouzianbandpey, S., Griffiths, D. V., Ibsen, L. B., Andersen, L. V. (2014). “Spatial correlation length of normalized cone data in sand: case study in the north of Denmark.” Canadian Geotechnical Journal, 51, 844-857. STATUS: Published Corrigendum: Spatial correlation length of normalized cone data in sand: case study in the north of Denmark S. Firouzianbandpey, D.V. Griffiths, L.B. Ibsen, and L.V. Andersen Ref.: Can. Geotech. J. 51(8): 844-857 (2014). dx.doi.org/10.1139/cgj-2013-0294. Figures 3 and 4 on pages 846 and 847, respectively, should be replaced with the figures shown herein. In Figs. 5a and 6a, on pages 848 and 849, respectively, “qt (MPa)” should be replaced with “Qt“. Tables 1 and 2 on page 850 should be replaced with the tables shown herein. In Tables 3 and 4 on p. 853, “Number of samples” should be replaced with “Number of samples*”, with the following footnote added below each table: “*In each sounding.” Table 1 Results of spatial variability of cone data for different soil layers at the Aalborg site.

		Soil type (Robertson 1990)
Cone parameter	Statistical parameters	Gravelly sand	Sands, clean sands	Silty sand, sand mixtures	Clayey silt to silty clay, silt mixtures
Normalized cone resistance	Number of samples	1109	2399	272	229
	COV (%)	38	33	26	21
	Mean	260.93	112.75	27.39	16.22
Normalized friction ratio	Number of samples	1109	2399	272	229
	COV (%)	65	51	61	46
	Mean	1.01	0.97	1.25	1.83

Table 2 Results of spatial variability of cone data for different soil layers at the Frederikshavn site.

		Soil type (Robertson 1990)
Cone parameter	Statistical parameters	Gravelly sand	Sands, clean sands	Silty sand, sand mixtures	Clayey silt to silty clay, silt mixtures
Normalized cone resistance	Number of samples	382	1999	1110	43
	COV (%)	56	47	13	21
	Mean	376.28	87.58	44.07	31.29
Normalized friction ratio	Number of samples	382	1999	1110	43
	COV (%)	48	25	23	35
	Mean	3.28	5.05	5.3	4.17

Received 23 May 2015. Accepted 19 June 2015. S. Firouzianbandpey, L.B. Ibsen, and L.V. Andersen. Department of Civil Engineering, Aalborg University, 9000 Aalborg, Denmark. D.V. Griffiths. Department of Civil and Environmental Engineering, Colorado School of Mines, Golden, CO 80401, USA; Australian Research Council Centre of Excellence for Geotechnical Science and Engineering, University of Newcastle, Callaghan NSW 2308, Australia. Corresponding author: S. Firouzianbandpey (e-mail: sf@civil.aau.dk). Fig. 3 Fig. 4

IS CITED AS: Firouzianbandpey, S., Ibsen, L. B., Griffiths, D. V., Vahdatirad, M. J., Andersen, L. V., Sørensen, J. D. (2015). “Effect of spatial correlation length on the interpretation of normalized CPT data using a Kriging approach.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE. DOI:10.1061/(ASCE)GT.1943-5606.0001358 STATUS: Published