A study of the correlation between soil-rock sounding and column penetration test data

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A study of the correlation between soil-rock sounding and column penetration test data

Johan Fransson

Master of Science Thesis 11/04 Division of Soil and Rock Mechanics

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Master of Science Thesis 11/04 Division of Soil and Rock Mechanics Royal Institute of Technology (KTH)

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Preface

This is the final thesis for my master degree as a civil engineer at the Royal Institute of Technology, Stockholm, Sweden. The idea for this thesis came from my supervisor Professor Stefan Larsson who has many years experience working with lime-cement columns both in his profession and at an academicals level. I worked closely with D. tech student Niclas Bergman, who helped me with general input, knowledge and his time. The thesis would never have been finished without the help from lecturer Pär Näsman at the Royal Institute of

Technology, who helped with the statistical aspects of this thesis, geotechnical engineer Gunnar Nilsson at NCC Teknik, who gave me some useful input about the total sounding method and its use with lime-cement columns, Anders Lundman at LCM, who not only helped with some well needed field trips but found one further test site to sound, field geotechnical engineers Hans-Ola and Ingemar Engström at Tyréns, conducted most of the soundings and came with great ideas and lastly my closest family, namely Thord, Inger, Shana and Emmin gave me moral support and help with some language aspects.

Johan Fransson, Stockholm 2011.

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Abstract

Lime-cement columns have been used in Sweden to improve poor soil conditions since the 1970’s. The method is inexpensive and flexible, but is difficult to test since the columns are manufactured in-situ. Many test-methods have been developed for testing the column strength during the years. Most of them need to be evaluated using an empirical correction-factor known as the cone factor. The column penetration test, KPS, is the most commonly used method in Sweden, it is considered to be reliable since a large part of the column cross-section is tested. The problem is that the probe easily deviates out of the column to the softer

surrounding soil. Today a pre-drilled guiding-hole, a soil-rock sounding, helps the probe to stay vertical. Although the soil-rock sounding is commonly not used for evaluation of column strength, the penetration resistance is recorded. A visual comparison between the plotted penetration resistances from the two methods shows similarities in both hard and soft areas of the columns.

The relation can be measured using statistics, such as the correlation coefficient. A strong correlation was also found, suggesting that a similar equation used to evaluate the undrained shear strength from the column penetration tests can be applied with the data from the soil- rock soundings. The statically pushed column penetration test probe and the rotated soil-rock sounding bit bore are likely to cause different failure modes in the column. This means that different empirical cone factors are needed when the undrained shear strength is evaluated.

By evaluating the ratio between the cone factors of the column penetration test and the data from the soil-rock soundings from three sites, E-road E18 north of Stockholm, E-road E45 outside Gothenburg and at a construction site at Lidingö, the following aspects of the ratio was investigated: if the ratio was site-specific; the sensitivity to the binder content; the sleeve friction and; the sensitivity to rotational speed and rate of penetration. Average columns formed from the penetration resistance at depth from each site were used during the evaluations.

The Swedish geotechnical society has standardised two methodologies that can be used for pre-drilling. The soil-rock sounding methodology which has no fixed rate of penetration or rotational speed, and the total sounding methodology, based on the Norwegian total sounding methodology which has fixed rate of penetration and rotational speed. The latter is to prefer when comparing results between sites.

To remove the sleeve friction, the data from the soil-rock soundings needed to be de-trended.

The amount of de-trending needed to find a constant cone factor varied at the sites between 0.5 kN/m and 1.0 kN/m. This however caused high interference, partly from scaling the variation. The cone factor for the total sounding methodology was found to be between 0.30- 0.45 times the cone factor for the column penetration test.

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Sammanfattning

Kalkcementpelare har använts i Sverige för att förstärka dåliga markförhållanden sedan 1970- talet. Metoden är billig och flexibel, men skapar sämre möjligheter för kontroll eftersom pelarna skapas in-situ. Många olika testmetoder har utvecklats för att kontrollera pelarnas hållfasthet under åren, men gemensamt för de flesta är att de måste utvärderas med en empirisk korrektionsfaktor kallad bärighetsfaktorn. Kalkpelarsonden, KPS, är den vanligaste metoden i Sverige. Den anses tillförlitlig eftersom den provar en stor area av pelaren.

Problemet är att den lätt styr ur pelaren till den kringliggande jorden som är betydligt lösare.

Idag förborras ofta sonderna med jord-bergsondering för att de inte ska styra ut. Trots att Jb- sonderingen idag inte används för att utvärdera KC-pelare registreras sonderingsmotståndet.

En visuell jämförelse mellan det plottade sonderingsmotståndet från KPS:en och dess förborrning visar tydliga likheter vad gällande hårda och mjuka partier i pelarna.

Likheten kan jämföras statistiskt med hjälp av korrelationskoefficienten. En stark korrelation hittades, vilket tyder på att en liknande ekvation som används för att utvärdera hållfastheten från KPS:en kan appliceras på data från Jb-sonderingen. Den fysiska skillnaden mellan metoderna där KPS:en trycks statiskt och jord-bergsonderingens borrstål roterar betyder troligen att olika brottsmoder inträffar i pelaren. Detta i sin tur betyder att den empiriska bärighetsfaktorn som används då pelarnas odränerade skjuvhållfasthet utvärderas sannolikt är skilda från varandra.

Genom att utvärdera förhållandet mellan KPS:ens och Jb-sonderingens bärighetsfaktorer från tre olika platser, E18 vid Stockholm, E45 utanför Göteborg samt ett bostadsområde på

Lidingö, kunde följande aspekter på förhållandet undersökas: hur platsspecifikt det var, känsligheten till bindemedelsmängd, påverkan av mantelfriktion samt rotationshastighet och sjunkhastighet vid borrandet. Då bäst korrelation mellan metoderna fanns när medelpelare skapades från penetrationsmotståndet över djupet användes dessa vid utvärderingen..

SGF har två standarder som används vid förborrning. Jb-sondering som saknar fast sjunkhastighet och rotationshastighet, samt totalsonderingen, baserad på den norska

totalsonderingen, som har fast sjunkhastighet och rotationshastighet. Den sistnämnda är att föredra när data ska jämföras mellan olika platser.

För att kompensera för mantelfriktion måste sonderingsmotståndet från förborrningen avtrendas. Mellan 0,5 kN/m och 1,0 kN/m behövde avtrendas för att få ett konstant

förhållande mellan bärighetsfaktorerna för Jb-totalsonderingen och KPS:en, detta skapade dock stora störningar, bland annat eftersom variationen förstorades upp. Bärighetsfaktorn för Jb-totalsonderingen var mellan 0,30–0,45 gånger bärighetsfaktorn för KPS:en.

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The need to develop less suitable areas, e.g. areas with poor soil conditions, such as low bearing capacity, creates geotechnical challenges. Piling with wooden-, steel- or concrete- piles is an option for buildings with a limited surface area. Roads and railroads have a far greater spatial extent which makes the majority of them unsuitable for piling. On top of this roads are commonly located in low-points, and those areas are in south of Sweden often covered by a layer of clay with low bearing capacity. This produced the lime-column method in the early 1970’s (Larsson 2005).

The mixing process when manufacturing the lime-cement columns are very complex (Larsson 2005). It involves many phases and factors that affects the result. Because of this it is not possible to estimate the strength of the columns prior to execution. Different test methods have been developed during the years. In common for most in situ tests is that they need empirical correlation between measured penetration resistance and true shear strength (Liyanapathirana and Kelly 2010). There is however still uncertainties about this correlation (Axelsson 2001). Absolute measured shear resistance may be obtained from unconfined compression tests or triaxial tests (Liyanapathirana and Kelly 2010). Since it is neither reasonable nor economically feasible to test entire column-sections at labs, these tests are performed on small samples that are likely not representing the entire column.

The most commonly used method for testing the strength of lime-cement columns in Sweden is the pre-drilled column penetration test (Larsson 2006, Axelsson and Larsson 2003), The reason is the large volume tested and the simplicity of the test. A special developed probe that spans almost the entire diameter of the column is pushed down into the column. This design of the probe is believed to reflect a better interpretation of the entire column width. The test can be performed in two manners, either by recording the resistance at the surface, meaning that the sleeve friction is also incorporated into the reading, or by using a modern cone penetration probe integrated with the column penetration probe which records only a small sleeve friction from the probe.

The big drawback with the column penetration test is that the large probe easily deviates to the surrounding soil. Axelsson and Larsson (2003) and Larsson (2006) suggest that the maximum depth at which the column penetration test can be utilised is as little as 8 meters even with columns with the modest undrained shear strengths of 150 kPa. Some methods have been suggested to deal with this problem, the reversed column penetration test have been developed where the probe is been pulled up through the column. The method was reviewed by Axelsson and Larsson (2003), which concluded that the installation of the probe disturbed the column why the evaluated results likely is not representing the surrounding columns and the usage of the reversed column penetration test in Sweden has since decreased. Another solution is to drill a guiding hole for the column penetration probe. By doing this, columns with a length of 12 to 15 meters and undrained shear strength of 300-350 kPa can be tested (Ekström 1994, Larsson 2006). Additional pre-drilling of the tests significantly increases the time consumption when testing, which turn increases the costs. Soil-rock sounding, in Sweden known as Jord-bergsondering is commonly used as pre-drilling.

A subjective visual comparison between the recorded penetration resistance from the column

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the columns. A more recent study (Jelisic and Nilsson 2005) examined the possibility to use the data from the pre-drilling, which was performed according to the total sounding

methodology to evaluate the strength of the columns. The study concluded that harder and softer areas correlated between the two methods when average columns were formed.

However the individual columns showed poor correlation.

Nilsson (2008b) later re-examined this as an internal report for the Swedish Transport

Administration, formerly known as Vägverket in an internal report. The report is unpublished, but with permission from the author it is summarized in the results section.

In this thesis the relation between the recorded penetration resistance from the soil-rock sounding and the penetration resistance from the column penetration test has been evaluated using statistics. Data from three sites was used. The idea was that the undrained shear strength of the columns could be evaluated via the penetration resistance from the soil-rock sounding with the equations used with the column penetration tests. The statistical evaluation included the coefficient of correlation to determine the relation, coefficient of variation to determine the variability and null hypothesis to make conclusions objectively.

If a sufficiently good correlation was found, the results from the soil-rock sounding could be used as a complement to the column penetration test for harder and longer columns where it is not possible to use the column penetration test. However the different failure modes of the column concerning a stationary probe or a rotating drill probably results in different cone factors for the two methods. This reasoning assumes that there exists a significant relation between the penetration resistance from the soil-rock sounding and the shear strength in the column.

A relation between the cone factors, used to evaluate the strength of the columns, from the column penetration test and the soil-rock sounding was compared between a test site at E-road E18, just north of Stockholm, one test site at E-road E45 outside Gothenburg and one test site at a construction project at Lidingö in Stockholm.

The Swedish soil-rock sounding (SGF 1999) does not suggest a rotational speed and rate of descent. This made it difficult to compare the penetrations resistance from different columns, since the penetration resistance likely depends on both rotational speed and rate of

penetration. The total sounding methodology (SGF 2006), which is mainly based on the soil- rock sounding however have both fixed rotational speed and rate of penetration. The pre- drilling was performed according to the soil-rock methodology at the E45 site and according to the total sounding methodology at the E18 site and the Lidingö site. This indicated whether the rotational speed and the rate of penetration had a major impact on the ratio of the cone factors.

Because more and more emphasis is put into the use of probability based design, for instance with the introduction of Eurocode 7, and thereby taking the variability into consideration, the variability with respect to the penetration resistance was evaluated. The variability is

important also when deciding how many column that needs to be tested in a control program.

The variability with respect to the coefficient of variation was compared between the column penetration test and the soil-rock sounding.

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Lime-cement columns

The lime-column method, also known as the deep mixing method DMM, was developed in Sweden and Japan in the 1970´s (Larsson 2005). In the beginning lime alone was used as binder in Sweden, but later cement was added to the mix to construct harder columns

(Larsson 2006). The methodology can be divided into mainly two sub-groups, the wet method and the dry method. The wet method was developed in Japan in the mid 1970’s. The dry method is often divided into the Japanese- and the Nordic method (Larsson 2005).

The dry method has solely been used in Sweden (Larsson 2006). It is most suitable for soft soils with a high natural water-content. The lime-cement mix is distributed into the soil through a mixing tool using pressurized air. The wet method uses a lime-cement slurry mixed above surface and pumped down to the mixing tool (Larsson 2005 and Larsson 2006). The wet method can be used in soils with lower natural water content and the slurry can have higher cement content (Larsson 2006).

Production

Specialised equipment is used to manufacture dry-mix lime-cement columns. The machine is usually based on a large excavator with a high boom (figure 1, left). The boom holds the long kelly bar with a mixing tool attached at the bottom. The mixing tool consists of wings or paddles covering the width of the column.

The lime-cement binder is normally premixed at the factory and transported to the worksite as a bulk cargo in a trailer. A smaller quantity is loaded onto the holding wagon (figure 1, right).

It is there kept under pressure between 200 and 1000 kPa (Larsson 2005) and fed to the

excavator using a pressure hose. The compressed air forces the binder down through the Kelly bar and is emitted from the mixing tool above the paddles.

The kelly bar is rotated and pushed to the desired depth of the column without any binder being incorporated. The rotation is then reversed and the speed is increased to about 150-200 rpm (Larsson 2005) and incorporates the binder into the ground, while the kelly bar is

retrieved at a speed of about 20-25 mm/s.

During the mixing process, depth, retrieving-rate, rotational speed, incorporated amount of binder as well as binder remaining in the holding wagon are measured and monitored (Carlsten 2000). The data from every column is recorded in a log-file.

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Figure 1. Lime-cement column production by LCM at Lidingö, Stockholm 2010.

Testing methods

Testing, sometimes known as quality assessment, can be divided into both testing that the design is fulfilled and to ensure the manufacturing process (Larsson 2005). Ensuring the manufacturing process is however not further discussed in this thesis. The aim of the columns determines which parameters are to be tested (Axelsson 2001). Axelsson also implies that almost all lime-cement columns in Sweden are used in mechanical problems, e.g. settlement- reduction or increased soil-stability, where the strength properties are of great interest (Larsson 2005), however there are also hydrological problems or environmental problems (Axelsson 2001) where permeability might be of greater interest. The undrained shear strength is the major parameter used to describe the strength of the columns (Larsson 2005).

A wide range of special probes have been developed to evaluate the undrained shear strength.

The most common test methods for soft to semi-hard columns in Sweden are according to Larsson (2006);

• Column penetration test (KPS)

• Pre-drilled column penetration test

• Reversed column penetration test (OPS)

• Pre-installed reversed column penetration test (FOPS)

• Vane tests And for harder columns

• Cone penetration test (CPT)

These methods are thoroughly described in The Swedish Deep Stabilizations Research Centre’s Rapport 17 (Larsson 2006). This thesis focuses on two testing methods, the column penetration test and the total sounding method. The column penetration test is performed using a cone penetration probe, CPT, integrated with the column penetration probe.

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Column penetration test and pre-drilled column penetration test (KPS)

The column penetration test, in Sweden known as traditionell pelarsondering, kalkpelarsond or KPS, is most widely used test method for lime-cement columns in Sweden (Larsson 2006).

It can be applied for 500 – 800 mm diameter columns, with a length of 8 meters and a

maximum undrained shear strength of 150 kPa. When harder or longer columns are tested, the probe often deviates from the column. If a guiding hole is pre-drilled it is possible to test longer columns with a maximum undrained shear strength of 300 – 350 kPa (Axelsson 2001, Larsson 2006). The probe is formed with two large wings that interact with almost the entire width of the column (figure 2, left). The width of the probe is usually 100 mm less than the diameter of the column. The probe to the left in Figure 2 is used with diameter 600 mm columns and has a width 500 mm.

Figure 2. Column penetration test probe (left), CPT probe (right).

The probe is pushed down with a constant rate of 20 mm/s ± 20 % and the penetration

resistance is registered (Carlsten 2000). If the penetration resistance it measured at the surface a reduction is have to be made for the sleeve friction, otherwise the strength of the columns will be overestimated (Axelsson and Larsson 2003). A more modern version of the column penetration test utilising the cone penetration test probe, CPT, integrated with the column penetration probe is sometimes used. The penetration resistance is recorded at the tip of the probe. Because of this almost no sleeve-friction is recorded when using a CPT probe. The undrained shear strength is evaluated using equation (1) (Larsson 2006).

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Equation 1. Evaluating the undrained shear strength

using KPS. (1)

c

fu N

A c = F

Where

fu =

c Undrained shear strength (Pa)

=

F Probe resistance force (N)

=

A Probe area (m²)

c =

N Empirical cone factor (-)

The empirical cone factor represents the correlation between the recorded force and the shear strength of the lime-cement column. The equation is simplification of the equation for the Swedish Geotechnical Institutes Iskymeter, a sounding method developed for soft soils (Axelsson 2001). A rigorous calibration of the Iskymeter was performed in Sweden between the 1930´s and the 1960´s. Axelsson and Larsson (2003) suggests a cone factor between 10 and 15.

Cone penetration test (CPT)

Cone penetration test uses a conic shaped probe that measures the cone penetration resistance and the local unit side friction (figure 2, right). It can be used on harder columns than the column penetration test, but a much smaller part of the column is tested (Larsson 2006). The CPT also has the disadvantage of easily deviate from the column.

The undrained shear strength can be evaluated using one of the equations (2), (Larsson 2006).

If the pore-water pressure is measured, with a Piezocone penetration test CPTU, the measured point pressure can be corrected to the total point pressure. Then the left equation is used.

Otherwise the right equation is used.

Equation 2. Evaluating the undrained shear strength

using CPT. (2)

kt v t

fu N

c q −σ ⁰

= or

c v c

fu N

c q −σ ⁰

=

Where

fu =

c Undrained shear strength (Pa)

t =

q Cone penetration resistance corrected for pore water pressure effects (Pa)

0 =

σv Initial total vertical overburden stress at the depth under consideration (Pa)

kt =

N Empirical cone factor for point resistance (-)

c =

q Cone penetration resistance and the local unit side friction (Pa)

c =

N Empirical cone factor for point resistance (-)

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The empirical factors N and _kt N are fairly uncertain for stabilized soil. Porbaha, Yamane _c and Taguchi (2001) suggest empirical factors between 18 and 23. Larsson (2006) states that values between 15 and 25 have been suggested for normal lime-cement columns and values up to 30 have been recommended for hard columns. The large uncertainties concerning the cone factors have been pointed out for instance by Larsson (2005).

The total sounding method (Jb-total sondering)

The total sounding method, in Sweden known as Jb-total sondering, is based on the

Norwegian total sounding method that was developed in the 1980´s (SGF 2006). It is a further development of the Swedish soil-rock sounding 2^nd class. The difference between the

Norwegian total sounding method and the total sounding is that the rate of penetration was lowered from 50 mm/s to 20 mm/s (SGF 2006), which is the same descent that is suggested for the CPT by the Swedish Geotechnical Society. The requirement to record the pressure of the spool medium was also removed.

The sounding is performed with a constant rate of penetration of 20 mm/s and a constant rotational speed of 25 rpm (SGF 2006). When the drill-rig has reached its maximum

penetration resistance, i.e. compressive force capacity, usually 10-30 kN, hammer-drilling is used. For softer lime-cement columns in Sweden hammer-drilling is not necessary since 10 kN of penetration resistance corresponds to a shear strength higher than most lime-cement columns when a 57 mm drill bit is used.

Figure 3. A button bit bore, 57 mm diameter.

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Test sites E-road E18

The initial statistical analysis was based on data from the E-road E18 between Hjulsta and Kista just north of Stockholm. The geotechnical data for the site is presented in table 1 (Karlsson 2008).

Table 1. Geotechnical data from the test site at E-road 18.

Layer Level Undrained

shear strength

Senstivity Natural water content

Liquide limit

Surface +8 m

Clay +7 m 30 kPa 4 70 % 80 %

Clay +6 m 9 kPa 3 55 % 50 %

Clay +5 m 12 kPa 5 >80 % > 80 %

Clay +3 m 9 kPa 6 60 % 50 %

Non-cohesive soil

+1 m Bedrock -4 m >

A test-area of 15 x 15 meter was selected for testing. The columns were placed in a grid pattern with a spacing of approximately 1 m. The 600 mm diameter columns were

manufactured with a binder content of 29 kg/m, 25 mm/s retrieval rate and a 100-200 rpm rotational speed. Thirty randomly selected columns were tested using pre-drilled column penetration tests (figure 4). The column penetration test was carried out using a CPT probe integrated with the 500 x 15 mm column penetration probe. Penetration resistance used while drilling and while pushing the column penetration probe was recorded to data-logs. The limited area made it possible to assume that the properties of the soil were approximately homogeneous.

Figure 4. Testing in progress at E18, March 2010.

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The guiding holes were drilled according to the total sounding methodology (SGF 2006) with a 57 mm button bit drill, a rate of penetration of 20 mm/s and a rotational speed of 25 rpm.

Great emphasis was however not put on maintaining the rotational speed which varied between 20 and 30 rpm, with a total average of 26.2 rpm. During testing all columns were between 16 and 20 days of age.

Residential area at Lidingö, Stockholm

JM AB has developed a residential area at Lidingö, north of Stockholm. LCM has performed the ground improvements. Lime-cement columns were installed to support the access roads during the later construction. Two test groups of four columns each were conducted in close proximity. The 600 mm diameter columns were manufactured using an average binder content of 23.5 kg/m and a rotational speed of 200 rpm. The columns were tested using pre- drilled column penetration test. The pre-drilling was performed according to the total sounding methodology and the column penetration test was performed using a CPT probe integrated in the column penetration probe. During the testing all columns were between 18 and 24 days old. It was also made possible to evaluate the sleeve friction from the total sounding tests. The total sounding methodology (SGF 2000) suggests that the drill can be lifted 0.5 m with constant rotational speed of 25 rpm and retrieval rate of 20 mm/s while the pulling resistance is registered, however this was not possible due to software limitations, instead the drill was lifted about 0.5 meter and pushed down a second time. The penetration resistance was then recorded over a distance of 0.5 meter, and an average sleeve friction per meter was calculated. Table 2 presents the geotechnical data from the site (Bard 2007).

Table 2. Geotechnical data at Lidingö

Layer Depth Undrained shear

strength

Filling ~1,5 m - - -

Clay 2 m 13 kPa 20 >80 %

Clay 3 m 12 kPa 24 76 %

Clay 5 m 15 kPa 20 62 %

Clay 7 m 20 kPa 20 65 %

Non-cohesive soil 10 m - - -

Bedrock 11 m - - -

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E-road E45

The Swedish Transport Administration was upgrading the existing roads and railroads on E- road 45 from Gothenburg to Trollhättan (Wahlqvist 2010). The road was heavily used and out-dated. The data used was taken from a pre-production test area. The geotechnical data for the test area is presented in table 3.

Table 3. Geotechnical data from E-road 45.

Layer Level Undrained

shear strength

Surface +2 m

Clay 0 m 12 kPa 11 100 %

Clay -2,5 m 15 kPa 31 92 %

Clay -5 m 17 kPa 30 73 %

Clay -7,5 m 20 kPa 28 72 %

Clay -10 m 18 kPa 33 60 %

Clay -12,5 m 16 kPa > 40 70 %

Clay -15 m 18 kPa > 40 68 %

A total of 21 columns were tested to evaluate the relation between the cone factors for the column penetration test and the soil-rock sounding. The area tested had three different binder contents that were tested. The binder content was 25-, 30- and 35 kg/m, with 7 columns each.

All of the columns were manufactured with a 600 mm diameter and a retrieval rate of 20 mm/s. The binder type was Lime-cement 50/50. The columns were all tested at an age between 12 and 16 days using pre-drilled column penetration tests. A column penetration probe with an integrated CPT probe was used. The pre-drilling was performed using soil-rock sounding (SGF 1999). It was performed with a rate of penetration of 30-40 mm/s until a penetration resistance of approximately 8 kN was reached, the rate of penetration was then lowered to prevent the drill rods from bending. Full rotational speed was used, which was about 50 rpm. The rotational speed dropped gradually as the sleeve friction increases by depth. During the pre-drilling a 58 mm drill bit was used.

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Methods

The data from the test sites was statistically evaluated to find the relation between the data from the column penetration test and the data from the soil-rock sounding. Using statistics, it was possible to quantify the relation. The use of a statistical tool known as null hypotheses helped to change the subjective conclusions to objective conclusions.

Before the evaluation the data was prepared using a visual inspection. The aim was to find singularities that came from changing drill rods. When the drill rods were changed, the data- log was paused and the first value was often almost zero when the drilling resumed. This was manually corrected.

The recorded resistance from both methods was synchronized at depth. The synchronization can be done by manually by visually lining up the data to match high strength areas and low strength areas. The correlation coefficient can also be calculated before and after shifting one data pair up or down. In this thesis the visual synchronization was primarily used, but when a visual interpretation was not possible the second method was utilized.

Statistical analysis

Some assumptions were made to make the statistical analysis possible. The data was firstly assumed to be normal distributed with a mean and a standard deviation. Secondly the data in the distribution was independent and random. It is an empirical fact that many physical quantities are normal distributed. (Blom et al. 2005). A common way to test for normal distribution is to use the Kolmogorov-Smirnov one sample test. Although the test is good for smaller data series it will not give a reliable answer for large data sets. The central limit theorem states that the distribution of X is approximately normal with the mean µ and variance σ² n when n is large (Johnson 2005). The distribution is normal when n is as low as 25 or 30. Since n in this case was much more than 30, it was assumed that the data was normal distributed. The data was also visually evaluated using histograms generated with PASW. The soil is likely not independent, there is a spatial correlation, which has earlier been investigated in a master thesis by Nilsson (2008a), but since the majority of the evaluation in this thesis was performed on average columns the assumption about randomness and

independence was valid.

The large amount of data made it difficult to calculate the statistics by hand why the statistical calculations were made in PASW Statistics 18 (formerly known as SPSS) and Microsoft Excel.

Coefficient of variation

The variation gave some indication of a measured value relative to the entire population. A low variation indicated that the population was uniform and any measured value was a good approximation of the population mean. The standard deviation is an absolute measurement of the variation, hence it depends of the scale of measurement (Johnson 2005).

The coefficient of variation, CoV is a measurement of the relative variation of a dataset compared to the mean value. The CoV gives the standard deviation as percentage of the mean

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Equation 3. Coefficient of variation (3)

%

⋅100 x s_x

Where

sx= sample standard deviation

x= sample mean

Correlation and correlation coefficient

Correlation is a measurement of the relation between two data series. It is used in science to understand how different physical quantities and phenomena relate. In this thesis the

relationship between the measured penetration resistances from the two tests, the column penetration test and the soil-rock sounding were investigated. When a correlation is found between two data series where there are no obvious relation a third variable, called a lurking variable (Johnson 2005) causes the correlation. This means that the two data sets have variables at a higher lever that is directly related. Since the two methods have physical

dissimilarities there was no obvious relation between them. The best candidate for the lurking variable that may cause the correlation is considered to be the strength of the soil.

The correlation between the column penetration tests and the soil-rock sounding has a true correlation coefficient ρ also known as the population correlation coefficient. This true correlation can never be measured, since the population is infinite. The best estimation of ρ is the sample correlation coefficient r that can be calculated (Johnson 2005). The same author states that r is not an unbiased estimator of the population correlation coefficient, but is widely used. This means that there might be a high correlation between the two test methods, although it is not easily measured since both tests are done in situ. When testing in situ, there are lots of interference obscuring the results. These can be weather related, human error, machinery error etc.

By plotting the two data sets against each other in a scatter plot, a visual impression of the correlation can be made. If the two data sets are (linear) related the points will form against a straight line in the plot. The better fit to the line the better correlation (figure 5). To get a mathematical interpretation of this, r can be calculated. This requires the data to be in standardized form according to equation (4).

Equation 4. Standardize data (4)

x i

s x x −

Where

xi = observation i x= sample mean

sx= sample standard deviation

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Equation 5: The Sample Correlation Coefficient (5)











 −







 −

= −

∑

= y

i n

i x

i

s y y s

x x r n

1 1

1

The correlation coefficient can take values between -1 and 1. The value 1 indicates a perfect positive linear relation, and -1 indicated a perfect negative linear relation. The value 0

indicates no linear relation and thus applies that the data sets have no linear relation (Blom et al. 2005). An r -value around 0.5 is usually considered a weak correlation (figure 5).

9 .

≈0

r r≈0.5 r≈0

Figure 5. Typical correlation coefficients.

Null hypotheses

A useful tool in statistics is the null hypothesis test. It is used to answer questions while dealing with uncertainties. A null hypothesis focus not on proving if a statement is true, but rather determines if it is probable that the statement is not true. Think of the phrase “Innocent until proven guilty”. When deciding if it is probable that the statement is not valid, a level of significance is chosen. The level of significance α is usually set to 0.05, 0.01 or 0.001, referring to the probability that the hypothesis was proven by chance or randomly (Blom et al.

2005). Table 4 present the most commonly used significance levels. At significance 0.05 five out of one hundred hypnoses are falsely rejected whiles at 0.001 level of significance only one out of one thousand hypotheses are rejected although they are true. Which significance is chosen depends on the consequences of making a false statement.

Table 4. The two-tailed significance levels 025

. 0 2=

α α 2=0.005 α 2=0.0005 σ

96 .

1 2.58σ 3.29σ

Quantity x

Quantity y

Quantity x Quantity x

Quantity y

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correlation coefficient can only take values between -1 and 1, a Fisher Z transformation was required to calculate the statistics (Johnson 2005). See equation (6).

Equation 6. Fisher Z transformation (6)

r z r

−

= + 1 ln1 2 1

The Fisher Z transformation forms a random variable having an approximately normal distribution with the mean

r r

z −

= + 1 ln1 2

µ 1 and the variance 3 1

−

n . This variable can then be used when calculating the statistics according to equation (7).

Equation 7: Statistics for the null hypothesis (7)

z n Z = −3⋅

The null hypothesis states that ρ equals zero, and was set up as follows:

1. The null hypothesis is thatρ =0. The alternate hypothesis is thatρ ≠0. 2. The level of significance α = 0.05 (table 4).

3. Criterion: Reject the null hypothesis if Z <−1.96or Z >1.96. 4. Calculations: The Z is calculated with equations (6) and (7).

5. Decision: If Z <−1.96or Z >1.96 the null hypothesis is rejected. It is then concluded that there is a relationship between the column penetration test and the soil-rock soundings at a 95 % significance level.

Confidence intervals for the correlation coefficient

The Fisher Z transformation above can also be used to determine a confidence interval for the ρ. z_a₂ refers to the level of significance (see table 4). The confidence interval then needs to be transformed back to r using equation (9) (Johnson 2005).

Equation 8: Confidence interval for the population

correlation coefficient (8)

3 3

2 2

+ −

<

− <

− n

z z n

z z^α µ_z ^α

(27)

Equation 9: Transformation back to r . ⁽⁹⁾







 + −

− + −







 + −

− + −









− −

−

− −









− −

−

− −

+

< −

<

+

−

3 3 3 3

2 2 2 2

n z z n

z z

n z z n

z z

n z z n

z z

n z z n

z z

e e

e r e

e e

α α α α

Hypothesis: two samples have an equal mean-value

The second null hypothesis focuses on the variation of the data sets. Since the sample

correlation coefficient is calculated using standardized data the mean value of the series is not taken into consideration. See equations (4) and (5). This means that although the variation correlates between the two data sets, the mean value can be different. Since one aim of this thesis is to find an empirical cone factor a null hypothesis has to be formed concerning the mean-values as well. The two populations have the mean µ₁ and µ₂and the variance σ₁² and

2

σ2 the null hypothesis µ₁ −µ₂ ≠0 is formed. The alternate hypothesis will then

beµ₁ −µ₂ =0. Since the samples are normal distributed and both data sets have nmore than 30 the following statistics in equation (10) can used (Johnson 2005).

Equation 10: Statistics for large sample test

concerning difference between two means (10)

2 2 2

1 2 1

2 1

n s n s

X Z X

+

= −

Where X is the sample mean and

sis the sample standard deviation

The null hypothesis was set up as follows:

1. The null hypothesis is thatµ₁ −µ₂ =0.

The alternate hypothesis is thatµ₁ −µ₂ <0 or µ₁ −µ₂ >0. 2. The level of significance α = 0.05 (table 4).

3. Criterion: Reject the null hypothesis if Z <−1.96 or Z >1.96. 4. Calculations: The Z is calculated with equations (10).

5. Decision: If Z <−1.96or Z >1.96 the null hypothesis is rejected. It is then concluded that the mean value of the two evaluated undrained shear strengths is not equal at a 95

% significance level.

Individual columns

The correlation coefficient was first calculated for the individual columns. The main reason to do this was to identify columns with low correlation. These columns were then investigated in

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Average column

In order to cancel out some of the individual variation in the columns an average column was formed. The average columns were formed as an average of the registered penetration

resistance from every column at each depth at one site. Calculating r gave an indication if the two methods related. A null hypothesis about the population correlation coefficient was formed and a confidence interval for the sample correlation coefficient was calculated.

The cone factors

The cone factor N_c is an empirical factor used for the evaluation of the undrained shear strength from the measured penetration resistance from the column penetration test. The equation to calculate the undrained shear strength is presented as equation (1). It was the authors believe that the same equation could be used to evaluate the undrained shear strength from the penetration resistance recorded while drilling. The total sounding method was calibrated against the column penetration test and a ratio of the cone factor between the column penetration test and the total sounding methodology was calculated. The equation to evaluate the undrained shear strength for both the column penetration test and the total sounding method are presented as equation (11).

Equation 11: Equations to evaluate the undrained

shear strength. (11)

(a) Column penetration test:

KPS c

KPS KPS

fu N

A F

,

τ =

(b) Total sounding method:

drill c

drill drill

fu N

A F

,

τ =

As suggested earlier the difference in failure modes between the methods likely means different cone factors are needed. By combining equation (11a) and (11b) a ratio between the cone factors could be formed as equation (12). If it was later found that if the same cone factor would apply to both methods this ratio would be one.

Equation 12: Relation between the cone factors (12)

KPS KPS drill drill KPS

c drill c KPS

c KPS KPS drill

c drill drill

F A A F N

N N

A F N

A

F = → = ⋅

, ,

Deviating column penetration probes

At the E45 site there were inclination data available from the column penetration tests. This made it possible with a good degree of accuracy to determine the amount of probe deviation from the column centre. Multiplying the tangent β for the inclination with the distance since

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Equation 13: Probe deviation (13)

( )

x z⋅ =∆

∆ tan β

Where:

βis the incline

∆z is the distance in z since last registration

∆x is the deviation in x since last registration

When the probe starts to deviate from the column centre the probe will gradually leave the column giving a value that is no longer fully representing the column. When the probe has deviated enough to stop representing the column is a subjective evaluation.

Evaluating the ratio of cone factors on three sites

Two additional sites were used to evaluate the ratio of the cone factors. This would dismiss the results as being coincidental. It would also prove if the ratio was site-specific. The data from all sites were first visually inspected. The r was then calculated for the individual columns. Average columns were then formed to evaluate both r and the variation, visually and calculated as CoV.

The construction area at Lidingö was chosen where the columns were tested with the specifications used at the E18 site. The way the total sounding test was executed at Lidingö also made it possible to evaluate the effect of the sleeve friction. During the execution of the total soundings the drill was lifted by 0.5 meters at the bottom of the bore holes and pushed down a second time. The idea was that this would be an estimation of the sleeve friction at that depth, why an average sleeve friction per meter was calculated for the individual columns and the removed as a linear function.

The construction of E-road 45 was chosen as a third location. At E45, the total sounding methodology was not utilized. As discussed earlier, the penetration resistance from the soil- rock sounding might not be compatible between sites, because the cone factors might be dependent on the rotational speed and/or the rate of penetration. Three groups of columns with different binder content were also tested. This made it possible to evaluate the effect of different binder content on the ratio of the cone factors.

The final evaluation of the ratios was done by plotting the ratios of all three sites as a function of depth.

De-trending

The penetration resistance was recorded at the surface during the soil-rock soundings, this meant that the sleeve friction generated from the drill rods was incorporated into the reading.

Since the sleeve friction is a cumulative quantity and the sleeve area is linearly related to the depth of the hole it was assumed to be linear distributed over the depth of the hole. This made it possible to remove the sleeve friction by de-trending the data using a linear function. The amount of de-trending needed was visually determined using the ratio of the cone factors,

(30)

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Results and discussion

The results are divided into two parts. The first presents the analyses of the correlation between the penetration resistances from the column penetration test and the soil-rock

sounding. The second part compares the ratio of the cone factors from all three sites based on average columns formed from each site.

Previous results from the use of soil-rock sounding

Nilsson (2008b) has previously investigated the use of the total sounding methodology with lime-cement columns. The report is unpublished but here summarized with permission from the author.

The test site was located at Lidatorp on road 73 from Stockholm to nearby Nynäshamn.

Twenty lime-cement columns, 800 mm diameter were manufactured. The columns were divided into four groups with specifications according to table 5.

Table 5. The groups of columns manufactured at road 73.

Group Columns Binder content Retrieval rate Rotational speed Length

1 5 80 kg/m³ 20 mm/s 200 rpm 13,5 m

2 5 80 kg/m³ 25 mm/s 200 rpm 13,4 -13,8 m

3 5 100 kg/m³ 20 mm/s 200 rpm 13,4 -13,8 m

4 5 100 kg/m³ 25 mm/s 200 rpm 13,5 -14,0 m

In each group two columns were tested after 7 days, two columns were tested after 14 days and 1 column was tested after 30 days. The columns were tested with the pre-drilled column penetration test. The guiding holes were drilled according to the total sounding methodology (SGF 2000) with a rotational speed of 25 rpm and a rate of penetration of 20 mm/s. If a penetration resistance of 20 kN was reached, hammer-drilling was used. The undrained shear strength was evaluated for the column penetration tests using a cone factor of 10. The same cone factor was also used to evaluate the undrained shear strength from the total sounding thus the ratio between the cone factors was 1. Some emphasis was also put on minimizing the sleeve friction. Every time the drill rod was spliced, the drill was lifted 0.5 m and the bore hole was lubricated with water.

The report concluded that there were a fairly good correlation between the column penetration test and the total sounding method when an average column were evaluated from group 1, group 2 and group 4. The correlation at group 3 was lower. However this might be explained by the difficulty to sound the 30-day column in that group. The author also points out that it was very hazardous to evaluate the undrained shear strength from individual columns using the total sounding methodology since the correlation of individual columns varied a lot.

The E18 site

The data was used to evaluate the correlation between the two test methods. Histograms for

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data sets are approximately normal distributed, thus making the following statistical evaluation valid.

Figure 6. Histograms calculated from the data at the E18 site.

The sample correlation coefficient for the individual columns is presented in figure 7. There are clearly a number of columns with high correlation coefficients around 0.8 and even 0.9. In fact the median value was 0.742. Eight columns had a correlation of less than 0.5 and four of those columns have an almost non existing correlation of 0.2 or less (column 26 had a negative correlation). All of the columns from the E18 site are presented in Appendix A.

r

Column penetration tests Soil-rock soundings

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Low-correlating columns

As shown in figure 7, columns 1,4,26 and 30 have an exceptionally low correlation

coefficient. The column penetration test and the guiding holes for column 1, 4, 26 and 30 are presented in figure 8. There is also an average based on all of the columns for comparison.

Since the earth pressure increases at depth, it was expected that the columns strength increases and accordingly the measured penetration resistance. This was observed for the evaluated average column for both the column penetration tests and the total sounding test (figure 8a).

This was also the case for all of the soil-rock soundings in columns with low correlation (although very slightly in column 30). However this was not the case for column 1, 4 and 26 where the penetration resistance for the column penetration test decreased while the

penetration resistance kept increasing for the total sounding tests. Since this was only occurring in the column penetration test it is the authors believe that this was caused by the probe leaving the column for the surrounding soil with lower strength. Columns 1, 4 and 26 were excluded from the subsequent analyses. The cause for the low correlation of column 30 could not be found, and it was therefore not removed from the study.

Soil-rock sounding Column penetration tests

a) Average columns 1-30

0

2

4

6

0 20 40

P e ne t ra t io n re s is t a nc e ( k N )

Depth (m)

b) Column 1

0

2

4

6

0 20 40

Depth (m)

c) Column 4

0

2

4

6

0 20 40

pth (m)

d) Column 26

0

2

4

6

0 20 40

pth (m)

e) Column 30

0

2

4

6

0 20 40

pth (m)

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Forming an Average Column

When plotting the average column penetration tests and the average total sounding tests a clear similarity was visible (figure 9). At the depth of seven meter, there was a sudden drop in penetration resistance for both methods. It was the authors believe that this was caused by either the end of the column or both the total sounding tests and the column penetration test deviating the column. At this depth the data was based on only two columns making it more uncertain. For this reason the average column was only be formed to a depth of seven meters.

At this depth, nine columns were present. When average columns were formed the r was calculated to 0.91. The correlation was null hypothesis tested. The null hypothesis states that the population correlation coefficient is zero, hence that there was no relation.

The null hypothesis was calculated using equations (6) and (7). This gave a Z -value of 26.4.

Since 26.4 was considerably more than 1.96, the null hypothesis was rejected. Calculating the confidence interval with equations (6), (7), (8) and (9) with a 95 % significance interval gave0.89< r<0.93.

The variation was also evaluated both by plotting the individual columns and by calculating the coefficient of variation, figure 9. It was concluded that the variation of the total sounding tests was generally five to ten percent points higher than the column penetration test. This might be caused by the smaller area tested.

All column penetration tests

0 1 2 3 4 5 6 7 8

0 10 20 30 40

P e ne t ra tio n re s is t a nc e ( k N )

Depth (m)

All total sounding tests

0 1 2 3 4 5 6 7 8

0 5 10

Depth (m)

Variance moving average 0.5 m

0 1 2 3 4 5 6 7 8

0 10 20 30 40 50 CoV (%)

Depth (m)

Average column All columns

Soil-rock sounding Column penetration test

Figure 9. Measured penetration resistance for all columns and average columns and CoV for both methods at E18.

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The Lidingö site

The r between the two tests methods were all above 0.5 for the individual columns at the Lidingö site. The median correlation coefficient was 0.73. Figure 10 presents r for all columns at Lidingö.

0 0,5 1

144 145 146 147 2595 2601 2603 2607 Colum ns

Correlation coefficient r

Figure 10. Sample correlation coefficient for individual columns at the Lidingö site.

When an average column was formed the correlation coefficient was 0.92, which indicated a high correlation. The 95 % confidence interval for the correlation coefficient is presented in table 6. The variation was evaluated by plotting the data from all columns and the CoV was calculated, figure 11. The CoV for the total sound tests was here considerably higher than the column penetration tests, but comparing with the E18 site the CoV for the total sounding test were fairly equivalent. The CoV for the column penetration test was however much lower at the Lidingö site.

Table 6. Results for the average column formed at the Lidingö site.

Sample correlation coefficient r 0.92

95 % confidence interval for r 0.90< r<0.94

Null hypothesis: There is no correlation Rejected ¹

¹ At a 95 % significance level

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All column penetration tests

2

3

4

5

6

7

0 10 20 30

P e ne t ra tio n re s is t a nc e ( k N )

Depth (m)

All total sounding test

2

3

4

5

6

7

0 2 4 6 8

Depth (m)

Variance moving average 0.5 m

2

3

4

5

6

7

0 10 20 30 40 50 CoV (%)

Depth (m)

Average column All columns

Soil-rock sounding Column penetration test

Figure 11. Measured penetration resistance for all columns and average columns and CoV for both methods at Lidingö.

The sleeve friction during the total sounding at Lidingö was also evaluated. This was possible since the drill was lifted about 0.5 m at the bottom of the holes and pushed down a second time. The sleeve friction varied among the individual holes between 0.4 kN/m and 1.3 kN/m with an average of 0.85 kN/m. At a depth between 5 and 6 meters on the average column formed, the sleeve friction accounted for 50 % of the penetrations resistance registered while drilling.

The E45 site

The correlation between the two methods was also evaluated on a site which did not utilise the total sounding methodology. The columns at the E45 site were formed into three groups constructed with different binder content, 25 kg/m, 30 kg/m and 35 kg/m. This would indicate the ratio of the cone factors sensitivity to binder content as well as rotational speed and rate of penetration. The effect of the binder content was distinguished by first comparing the cone factor-ratios between the three groups.

Visually comparing the penetration resistance gave the clear indication that there was a low correlation at very shallow depth. This was likely caused by the methods not correlating at the dry clay crust above the water table. There was also a low correlation at higher depth where the penetration resistance from the column penetration test decreased at a depth around 7-8.

A study of the correlation between soil-rock sounding and column penetration test data