In-situ Penetration as Alternative to Extensive Boreholes and

Lab Testing for Exploration in Sandy Soils

Mwajuma Ibrahim Lingwanda

Licentiate Thesis

Department of Civil and Architectural Engineering

Division of Soil and Rock Mechanics

Royal Institute of Technology

Stockholm, 2015

iii

Preface

This research work was pursued in the period between April 2012 and December 2014 at the

Division of Soil and Rock Mechanics, KTH Royal Institute of Technology and University of Dar es

Salaam, Tanzania particularly the Department of Transportation and Geotechnical Engineering in

the College of Engineering and Technology. The work was closely supervised by Professor Stefan

Larsson of KTH who was assisted by Dr Dalmas L. Nyaoro of University of Dar es Salaam.

The research is part of Rural and Urban Infrastructure Development Program conducted in

Tanzania and funded by Swedish International Development Cooperation Agency (Sida). Their

financial support is highly appreciated. In connection, I would like to express my gratitude to the

management of the department of Transportation and Geotechnical Engineering for giving me the

opportunity to be part of the Sida funded program and to the Principal of Mbeya Institute of Science

and Technology for allowing me the time to pursue the research.

I would like to extend my acknowledgement to the supervisors Professor Stefan Larsson and Dr

Dalmas Nyaoro for the guidance, support and motivation throughout the study. I had an

opportunity to learn a lot from each of them apart from matters relating to this particular research

work.

My sincere gratitude also goes to Mr Juma and his group for their participation in the laborious

field work activities. Laboratory technicians at the Soil Mechanics Lab, University of Dar es Salaam

are equally thanked for their assistance in conducting the lab tests. I also thank my colleagues at

the Department of Transportation and Geotechnical Engineering especially Ms Motta Kyando for

her contribution in making the data collection process possible.

To my colleagues at the Division of Soil and Rock Mechanics, I would like to thank everyone for

their contribution especially during the constructive seminars. It has been a pleasure to have the

opportunity to participate in such a productive and wonderful group.

Lastly, to my family, brothers and sisters for their love and support. Each one of you has

contributed in a way to my academic achievement. My mother Asia, father Engineer Ibrahim, son

Isaac and in a special way to my beloved husband Issa for his encouragement and patience.

Dar es Salaam, December 2014

Mwajuma Lingwanda

iv

Abstract

Geotechnical investigation is an important part of rural and urban infrastructure development. The

cost of which is a significant part of a construction project, therefore it should be of concern. Any

program or research to assist reduction of geotechnical investigation cost is valuable and should

be appreciated. In Tanzania, the most commonly used method for site exploration is the standard

penetration test (SPT) accompanied by bore-holing and laboratory testing of retrieved samples.

However, this method is expensive in monetary and time cost. Consequently, in attempt to save

time and money, a few number of tests are normally executed for site investigations. When it is

necessary to increase the scope of investigation, geotechnical engineers normally supplement

the bore-holing with a cheaper and much quicker method, the light dynamic probing (DPL).

Through this research, the static cone penetration test (CPT) has been introduced to enable

collection of larger amount of data in a shorter time and reduce the cost of data acquisition. Both

the SPT and CPT are very popular in the world as compared to the DPL.

Determination of soil design values in geotechnical engineering normally relies on established

relationships between measured values and desired soil design parameters. As a result, there

exist various empirical correlations between soil test results and design values. In-situ and

laboratory tests are the major categories of soil testing methods. Although the light dynamic

probing has been in use for quite some time in Tanzania, there are no published local relationships

between its data and soil design values. This makes it underutilized in the sense that data

collected with it are only applicable for site stratification purposes. The need to increase

usefulness of DPL values for design is one objective of this study. The approach adopted to fulfil

this objective is to establish relationships between results of DPL and those from the popular

methods of SPT and CPT.

The geotechnical community has long been aware of uncertainties induced in the design systems

due to variations in soils and loads properties, inaccuracies in design equations, errors in

measurements and in the construction process. Traditionally, at the design stage, the engineer

relies on factors of safety to reduce the risk of adverse effects. This is done without a separate

evaluation of each of the factor contributing to the uncertainty. A global safety factor is assigned,

therefore subjective. Reliability based design (RBD) is a relatively new concept of structural safety

which provide a consistent evaluation of design risk using probability theory. Essential to its

application, is the quantification and consideration of uncertainties involved. Quantified

uncertainties of soil parameter values may also find application in evaluating effectiveness of soil

exploration programs.

A rather extensive soil exploration was performed on a sandy soil in Dar es Salaam where CPT,

DPL, SPT and samples were collected for laboratory testing. With the information gathered,

empirical correlations were established between CPT and DPL data, SPT and DPL data, as well

as between CPT and SPT data. Based on the coefficient of regression and the transformation

uncertainties, DPL to CPT transformation appears better than DPL to SPT transformation,

therefore recommended for use. Geotechnical uncertainties associated with CPT, DPL and SPT

methods were quantified and compared to uncertainties in determination of soil secant

constrained modulus (𝑀𝑠) obtained directly from the oedometer test. In order to establish

transformation model uncertainties, correlations were established between 𝑀𝑠 and the in-situ

measurement data. Results indicates that the three in-situ methods are associated with similar

order of magnitudes of total uncertainties in predicting 𝑀𝑠 which are about twice as much as

uncertainties in obtaining 𝑀𝑠 directly from the oedometer test. For further studies, it is

recommended to determine the consequences of the quantified uncertainties to a designed

foundation.

v

Sammanfattning

Kostnaden för geotekniska undersökningar, vilket är en icke försumbar del av ett byggprojekt,

därför bör det vara av intresse. Alla program eller forskning för att hjälpa minskning av geoteknisk

undersökning kostnaden är värdefull och bör uppskattas. I Tanzania är den vanligaste metoden

för geotekniska undersökningar standardpenetrationstest (SPT) åtföljd med provtagning och

efterföljande laboratorieförsök. Dessa metoder är dock tidskrävande och dyra. När det är

nödvändigt att utöka omfattningen av undersökningar så kompletterar man ofta med snabba och

billigare metoder såsom lätt dynamisk sondering (DPL). En betydligt vanligare metod som dock

inte använts i Tanzania är statisk spetstrycksondering (CPT). Ett syfte med föreliggande studie är

att introducera CPT i Tanzania och studera korrelation med SPT.

Utvärdering av dimensionerande värden för jordmaterial från fält- och laboratoriemetoder förlitar

sig ofta på etablerade empiriska relationer Trots att den lätt dynamisk sonderingsmetoden (DPL)

använts i Tanzania sedan länge, så saknas det tillförlitliga studier där man korrelerat

sonderingsresultat mot data från laboratorieförsök. Osäker metodik för utvärderingen av resultat

har gjort att metoden bara används för att bedöma jordlagerföljder. Ett ytterligare syfte med

studien är att etablera empirisk korrelation mellan data från DPL och mer etablerade metoder

såsom SPT och CPT.

Mätdata och utvärderade parametrar från geotekniska undersökningsmetoder är behäftade med

mer eller mindre stora osäkerheter. Som oftast förlitar sig ingenjörer idag på erfarenhet och att

sökerhetsfaktorertar hand om sådana osäkerheter. Detta görs dock subjektivt och utan att

separera utvärderingen av de enskilda osäkerheterna. Sannolikhetsbaserad dimensionering är

för geotekniska tillämpningar en relativt ny dimensioneringsfilosofi som möjliggör beaktande av

faktorer som bidrar till osäkerheter. Utvärdering av osäkerheter kopplade till olika

undersökningsmetoder gör också att man kan värdera olika undersökningsprogram och därmed

effektiviteten.

En relativt omfattande geoteknisk fält- och laboratorieundersökning är utförd på en sandig jord i

Dar es Salaam. Undersökningen omfattade CPT, DPL, SPT och laboratorieförsök på upptagna

jordprover. Empirisk korrelation mellan de tre sonderingsmetoderna är utvärderad och

osäkerheterna är kvantifierade och diskuterade i relation till utförda ödometerförsök. Resultaten

indikerar att de tre metoderna är associerade med osäkerheter i samma storleksordning med

avseende på utvärdering av ödomermodulen. Ten totala osäkerheten är i storleksordningen

dubbelt så stor som osäkerheterna relaterade till utvärdering av ödomermodulen direkt från

ödometerförsök. För vidare studier så rekommenderas det att uppskatta konsekvenserna av de

kvantifierade osäkerheterna på en design av en grundläggning.

vi

List of publications

This licentiate thesis is based on work presented in three publications as listed below:

Paper I Lingwanda, M. I., Larsson, S. and Nyaoro, D. L. 2014. Correlations of SPT, CPT and DPL data for sandy soil in Tanzania. Geotechnical and Geological Engineering

Paper II Lingwanda, M. I., Larsson, S. and Nyaoro, D. L. 2014. Inherent soil variability linked to different characterization methods. In proceedings of Sida Annual Regional conference, Entebbe, July, 2014

Paper III Lingwanda, M. I., Larsson, S., Prästings, A. and Nyaoro, D. L. 2014. Comparison of geotechnical uncertainties linked to different soil characterization methods. Geomechanics and Geoengineering: An International Journal

The author of this thesis did the planning of field works, participated in the field and laboratory

works, analysed the measured data, and did the calculations, graphing and writing work all under

the supervision of the co-authors Larsson and Nyaoro. The co-author Larsson closely supervised

the calculation work as well as shaping the papers through critical discussions conducted time to

time therefore has contributed to the great extent of the final products. Co-author Nyaoro

contributed much during conduction of field and laboratory works while co-author Prästings

contributed intellectually to paper III.

vii

List of notations and abbreviations

The following symbols and abbreviation appear in the thesis

Roman letters

𝑎 Net area ratio

𝐵 Bulk modulus

𝐵𝑞 Pore pressure ratio

𝐶𝑂𝑉 Coefficient of variation

𝑑 Diameter of load cell support

𝐷 Projected diameter of the cone

𝐷50 Mean grain size

𝐸 Young’s modulus

𝑓 Model constant

𝐹% Percentage of fines content in a soil

𝐹𝑟 Stress normalized friction ratio

𝑓𝑠 Sleeve friction

𝐹𝑠 Factor of safety

𝐺 Shear modulus

𝐼𝑐 Soil behaviour index

𝐿 Size of the failure domain

𝑀 Constrained modulus

𝑀𝑖 Initial tangent constrained modulus

𝑀𝑠 Secant constrained modulus

𝑀𝑡 Tangent constrained modulus

𝑛 Number of simulations

𝑁 Number of blows per 300 mm penetration for SPT

𝑁10 Number of blows per 10 cm penetration for a dynamic probing

𝑁60 SPT-𝑁 value corrected with respect to energy

𝑃𝐼 Plasticity index

𝑝𝑓 Probability of failure

�̂�𝑓 Typical probability of failure

𝑞𝑐 Cone resistance

viii

𝑞𝑡 Cone resistance corrected for unequal end area effects

𝑄𝑛 Stress normalized cone resistance

𝑄 Foundation load

𝑅 Resistance to load

𝑠 Strain

𝑠𝜀 Standard deviation of transformation uncertainty

𝑆𝐷 Standard deviation

𝑆𝑀 Safety margin

𝑢 Pore water pressure

𝑈4/𝑈100 Sampling tube of diameter 4 inch/100 mm

𝑉𝑎𝑟(∙) Variance

𝑋 Measured property

�̅� Average property

Greek letters

Γ2 Variance reduction factor

Φ−1(∙) Inverse standard normal cumulative function

𝜎´ Effective stress

𝜎𝑣𝑜 Original overburden stress

𝛼 Model constant

𝜀 Transformation model uncertainty

𝜃 Scale of fluctuation

Abbreviations

CPT Cone Penetration Test

DPH Heavy Dynamic Probing

DPL Light Dynamic Probing

DPM Medium Dynamic Probing

RBD Reliability Based Design

SPT Standard Penetration Test

ix

Table of Contents

Preface ........................................................................................................................................................ iii

Abstract ...................................................................................................................................................... iv

Sammanfattning ........................................................................................................................................ v

List of publications .................................................................................................................................. vi

List of notations and abbreviations ................................................................................................... vii

Table of Contents ..................................................................................................................................... ix

Chapter 1 – Introduction .........................................................................................................................1

1.1 Background ..................................................................................................................................1

1.2 Research objectives and significance ......................................................................................2

1.3 Outline of the thesis ....................................................................................................................2

Chapter 2 – In-situ tests and correlations between data ................................................................3

2.1 Advantages of in-situ tests over sampling and lab testing ....................................................3

2.2 Cone Penetration Test (CPT) ....................................................................................................3

2.3 Standard Penetration Test (SPT) .............................................................................................4

2.4 Light Dynamic Probing test (DPL) ............................................................................................5

2.5 General observations for data collected in-situ ......................................................................5

2.5.1 Skin friction effect on DPL ..................................................................................................5

2.5.2 Effect of soil type on SPT results ......................................................................................7

2.5.3 Effect of overburden stress on in-situ test results ..........................................................7

2.6 In-situ tests influence zones ......................................................................................................8

2.7 Previous correlations ..................................................................................................................8

2.7.1 CPT – DPL and SPT – DPL correlations .........................................................................8

2.7.2 CPT – SPT correlations ......................................................................................................9

Chapter 3 – Soil modulus and its determination ........................................................................... 11

3.1 General ...................................................................................................................................... 11

3.2 Types of soil moduli ................................................................................................................. 12

3.3 Determination of constrained modulus ................................................................................. 12

3.4 Correlations with in-situ tests.................................................................................................. 13

Chapter 4 – Geotechnical uncertainties and their determination ............................................. 15

5.1 Sources of uncertainties .......................................................................................................... 15

5.2 Evaluation of uncertainties ...................................................................................................... 16

5.3 Variance reduction ................................................................................................................... 16

x

5.4 Importance of quantifying uncertainties ................................................................................ 17

Chapter 5 – Consequences of uncertainties .................................................................................. 18

5.1 Importance of evaluating the consequences of uncertainties ........................................... 18

5.2 Computation of failure probability .......................................................................................... 18

5.3 Input to the performance function .......................................................................................... 19

5.4 Comparing probabilities of failure .......................................................................................... 20

Chapter 6 – Summary of appended papers .................................................................................... 21

6.1 Paper I ........................................................................................................................................ 21

6.2 Paper II....................................................................................................................................... 21

6.3 Paper III ..................................................................................................................................... 22

Chapter 7 – Conclusions and recommendations .......................................................................... 23

References ............................................................................................................................................... 24

Appended Papers ................................................................................................................................... 29

1

Chapter 1 – Introduction

1.1 Background

Before construction of a foundation for a civil engineering structure, the two major phases of a

geotechnical undertaking are; determination of design soil parameters through site investigation

and foundation design. In the first phase, geotechnical investigation is performed with in-situ

and/or laboratory testing of samples retrieved from the respective area. In practice, the test results

are then manipulated to determine soil design parameters normally through previously established

empirical correlations. There are numerous accepted in-situ testing methods to determine details

of the subsurface conditions with respect to foundation design. The standard penetration test

(SPT) and the cone penetration test (CPT) are most common and popular methods worldwide.

The light dynamic probing (DPL) method is not as popular as compared to SPT and CPT but is

quite common for site stratification in Tanzania. A very comprehensive history and development

of these in-situ methods was recently given by Massarsch (2014). Laboratory testing methods are

of different categories and their selection depend mainly on the type of information desired for a

particular design.

In relation to determination of soil design parameters, the current practice in Tanzania is to perform

SPT accompanied with sampling for further laboratory testing. This practice is known to be costly

in time and money, as a result, limited investigation scopes are normally performed in attempt to

save money. According to Temple and Stukhart (1987), inadequate geotechnical investigation is

the number one source of costly, overdesigned foundations, project delays, disputes, claims and

project cost overruns therefore need proper attention. Consequently, in such situations,

geotechnical engineers are tempted to reduce the risk of failure by over-designing the foundations

(Parsons and Frost, 2002; Jaksa et al., 2003). A common approach in Tanzania for increasing the

amount of information at affordable cost is to perform the cheaper and much quicker DPL as a

supplement to SPT. However, DPL results are limited to site stratification use as there are no

previously established relationships between soil design values and its data as opposed to the

more popular SPT and CPT methods. Before this research, the CPT was yet to be introduced to

practitioners in Tanzania and it is one of the objectives of the research to introduce the method.

Geotechnical engineers in Tanzania still apply the traditional total factor of safety method for

designing of geotechnical structures. Subjectively, a global factor of safety between 2 and 3 is

normally applied to accommodate the effects of uncertainties to the designed foundations.

Reliability based design (RBD) is a relatively new concept of safety which basically provide a

consistent evaluation of design risk using probability theory. Essential to the application of RBD is

the quantification and consideration of uncertainties involved. Quantified uncertainties of soil

parameter values may also find application in evaluating effectiveness of soil exploration

programs. Different soil investigation methods may be associated with different magnitudes of

uncertainties. Their quantification and comparisons will aid in decision making when it comes to

selecting one investigation method out of the available ones. In general terms, the CPT is

considered superior to the SPT in terms of quality of information gathered. There is even

suggestions to abandon the SPT as investigation method on the basis of its crudeness

(Robertson, 2012). A rational comparison of uncertainties between information gathered with

different methods together with their consequences to the final design will shade light to the extent

of effects of method choice on the cost of designed foundation in addition to the ordinary practice

of considering only time and cost of executed method when deciding the type and scope of

geotechnical investigations.

2

1.2 Research objectives and significance

The main objective of this research is to achieve cost effective geotechnical investigation with

application of in-situ methods but without sacrificing the quality of information gathered. As

geotechnical engineers are experienced in using SPT and lab obtained data for design, the

proposal of relatively new methods such as CPT and DPL data to be incorporated in designs

should come hand in hand with understanding of the consequences. Three specific objectives

were set to be studied;

I. Determining relationship between data from the three in-situ methods considered in the study.

SPT – CPT relationships are common in literature but SPT – DPL and CPT – DPL are

uncommon. After the relationships are established with the statistical quality determined,

recommendation shall be made on the best way of intermediate transformation of DPL data

to design values. In addition, SPT – CPT relationship shall be compared to those existing in

literature and commented on.

II. Quantifying uncertainties related to soil testing methods

A comparison of uncertainties linked to the in- situ methods is a rational way of determining

how each method can accurately predict a desired soil design value from the measured

values. A laboratory method shall be selected to provide a benchmark for the comparison.

Since the last decade, the geotechnical community has seen an increased interest in the

application of RBD for geotechnical structures. Studies related to RBD application at different

soil conditions and methods of investigation have been conducted and reported. The

quantified uncertainties may save as inputs to reliability based design problems in similar

geotechnical conditions as such information is normally not readily available in ordinary

geotechnical projects due to limitation in investigation scope. Studies of this nature are

demanded as they provide information and a room for improving analytical methods. As

recently remarked by Ching and Phoon (2014), characterization of geotechnical variability is

still an immature research area.

III. Determining the impact of geotechnical uncertainties to final designed foundations

To determine the effects of a selected soil investigation method to the designed foundation, it

is decided to quantify the consequences of the uncertainties. This shall be done through a

foundation design case study where data from the four different soil investigation methods

shall be used as inputs to a foundation settlement prediction problem using RBD. The

observed outputs shall be compared and conclusion drawn about the effect of employing each

individual method in obtaining foundation design data.

1.3 Outline of the thesis

This thesis comprises of two main parts; the research summary and three appended papers. The

summary is presented in seven chapters. The first chapter is the introduction to the research in

general which basically is the background, objective and significance of the research. The second

chapter is about understanding the in-situ methods involved in the research and existing

relationships between their data. The third chapter is about the laboratory method that was chosen

as the benchmark for comparing uncertainties, the oedometer test, particularly determination of

soil modulus through it. The fourth chapter describes the types of geotechnical uncertainties

studied under this research and the methods of determination. The fifth chapter describes briefly

about what shall be done to fulfil the third objective which is basically the PhD phase. In chapter

six, a brief explanation of what is found in the appended papers is provided. Finally, conclusion

and recommendations are presented in chapter seven.

3

Chapter 2 – In-situ tests and correlations between data

2.1 Advantages of in-situ tests over sampling and lab testing

In-situ test provide efficient and economical means for determining the subsurface profile

information and specific property data required for the design of foundations. Several benefits can

be realized by employing in-situ techniques as compared to sampling and laboratory testing.

Orchant et al. (1988) highlighted the benefits of using in-situ method as:

i They can be used in soils which are difficult to sample such as saturated sands without

causing significant sample disturbance.

ii They allow materials to be tested in their existing state of stress and natural environment

avoiding the influence of sampling, transportation, and storage which sometimes make it

difficult to create this conditions in the laboratory. Obtaining soil property data in its natural

stress state and environment is important to best predict foundation response to the

applied loads.

iii Some in-situ methods such as the CPT provide a continuous record of the soil profile thus

increasing the probability of predicting layer boundaries and the geological details more

accurately.

iv With in-situ tests a larger volume of soil is tested than in most laboratory tests and the

results better reflect the influence of the soil structure on the designed foundation.

v In remote locations, transporting undisturbed samples to a laboratory for testing may pose

a challenge, making in-situ tests an attractive option in such cases.

vi In-situ test results may be interpreted on site allowing for immediate performance of

addition tests where necessary.

The applicability of a given test method depend on several factors. The most important one is

ability of the test to provide the necessary information to enable foundation design. Other factors

include the geological conditions of the tested area, availability of equipment, project

requirements, method of analysis intended for the design, range of soil conditions for which the

test is suited, access requirements and cost of performing the test.

2.2 Cone Penetration Test (CPT)

The static cone penetration test or simply the cone penetration test is carried out by hydraulically

pushing a 60o cone of area 10 cm2, diameter 35.7 mm into the ground at a constant speed of 2

cm/s while measuring the force necessary to push. In addition to measuring the cone resistance

(𝑞𝑐), the shear force on a 150 cm2 friction sleeve with the same outer diameter as the cone and

located immediately above the cone, is also measured as (𝑓𝑠). The penetration rate is an important

factor that affect the results and have been studied for example by Kim et al. (2008). In a normal

operation, the cone is driven from the ground surface with a penetration rig without bore-holing.

CPTs are either of mechanical friction case or electric penetrometers. In the electric cone,

measurements are made using strain gauges or transducers located immediately above the cone.

The modern electronic CPT equipment is considered to be operator independent and is capable

of measuring not only 𝑞𝑐 and 𝑓𝑠 but also other parameters such as pore pressure (in piezocones),

cone inclination and soil sensitivity depending on the manufacturer. According to Robertson

(2011), most commercial CPT cones are capable of penetrating very hard soils and even soft

rocks. In comparison between the two common measurements with CPT, 𝑓𝑠 is generally less

accurate as compared to 𝑞𝑐 (Lunne et al., 1997; Robertson, 2011) due to design differences and

tolerance. This study generally utilized 𝑞𝑐 values. The speed and convenience with which modern

4

electric cone equipment are used has led to its adoption in many counties. In this study, the

equipment used was a portable, 150 kN force, electic piezocone operated by a standalone pusher

as presented in Figure 1.

Some studies recommend the correction of tip resistance 𝑞𝑐 to 𝑞𝑡 using equation 1, to account for

unequal end area effect. However, in this study, measured 𝑞𝑐 values were used directly as the

difference between 𝑞𝑡 and 𝑞𝑐 was very small in the tested dry sandy soil, an observation also

reported by Robertson (2010) for non-soft fine soils.

𝑞𝑡 = 𝑞𝑐 + (1 − 𝑎)𝑢

𝑎 = 𝑑2

𝐷2

1

where

𝑢 = pore water pressure

𝑎 = net area ratio

𝑑 = diameter of load cell support

𝐷 = projected diameter of the cone

A similar correction is normally applied to measured sleeve friction.

When advancing, the cone tip forces a passive failure in front of it and the instrumented tip senses

soil resistance about 5 to 10 cone diameters (Rogers, 2006) ahead and behind the advancing tip.

This phenomenon is important to note especially when the cone advances through a thin soft

material imbedded in stiffer soil as will register falsely high values of cone resistance.

Relative to other soil exploration methods, the CPT has the advantage of providing large volume

of information within short time and low cost. However, the most outstanding disadvantage is the

disability to draw samples for laboratory testing. The CPT is considered to have small

measurement errors, lower than other in-situ methods and many laboratory methods (Robertson,

2011).

2.3 Standard Penetration Test (SPT)

The SPT is known to be the most widely used geotechnical characterization test worldwide (Daniel

et al., 2003). The test is performed by driving a standard split spoon sampler in boreholes using

repeated blows of a 63.5 kg hammer falling through a 760 mm height. The hammer is connected

to the split spoon through rods and it is operated above the borehole. Having lowered the split

spoon to the bottom of the borehole, it is then driven a distance of 450 mm while counting the

blows in 75 mm intervals of penetration. The number of blows per the last 300 mm of penetration

are recorded as the 𝑁 value while discarding the top 150 mm blows for reasons of soil disturbance

during boring.

The energy delivered to the split spoon in theoretically the free fall energy of 63.5 kg mass falling

through the 760 mm height. In practice, some of the energy is lost in the process, due to among

other reasons, the hammer not lifted for the full 760 mm. There are different types of SPT hammers

in use worldwide including the hand-lifted hammers, slip rope hammers, hand-controlled trip

hammers and the automatic trip hammers which are so far the best type of hammers because of

the consistency in energy delivered per blow. In this study, an automatic trip hammer was used

to operate the SPT, part of the equipment is indicated in Figure 1.

5

The SPT may be regarded as both, an in-situ test (when taking 𝑁 values) or a sampling method

as it allows collection of disturbed samples in the boring process, undisturbed samples through

special tubes named 𝑈4 or 𝑈100 samplers and disturbed samples from the split spoon. The split

spoon has an outside diameter of 51 mm and an inside diameter of 35 mm.

The most important factor that affects SPT 𝑁 values is the energy that actually drives the sampler.

This energy is influenced by such factors as hammer weight, height of fall, type of hammer as well

as type and size of driving rods. The importance of driving energy has long being appreciated and

has triggered many studies on the area such as Schmertmann and Palacios (1979), Bosscher

and Showers (1987), Yokel (1989), Morgano and Liang (1992), Drumright et al. (1996), Abou-

matar and Goble, (1997), Daniel et al. (2005), Youd et al. (2008), Lee et al. (2010). Being the

average historical energy recorded from different operators (Daniel et al., 2003), 60% of the

theoretical hammer energy is considered the standard energy for harmonizing SPT 𝑁 values and

is also recommended by Skempton (1986). The energy corrected 𝑁 value is presented as 𝑁60 .

The device used in this study was the high efficiency (Drumright et al. 1996, Youd et al. 2008)

automatic trip hammer. The specific hammer used for this study has an efficiency 71% as

measured during calibration by the manufacturer. Both CPT and SPT values have been correlated

with many soil design parameters e.g. in Kulhawy and Mayne (1990).

2.4 Light Dynamic Probing test (DPL)

Dynamic probing is the oldest method of ground penetration for exploration purposes of

foundation engineering. Due to simplicity of the test, there are a variety of dynamic probing

equipment used worldwide. When the equipment are classified in terms of hammer weight, the

light dynamic probing is the one with a hammer of 10 kg or less. Others are heavy dynamic probing

(DPH) and medium dynamic probing (DPM). In operating the DPL, the weight is dropped

repeatedly through a 50 cm height and the number of blows to cause a 100 mm penetration is

recorded as 𝑁10. A cone of diameter 25.2 mm or 35.7 mm is attached to roads of 22 mm outer

diameter. The equipment used in this study complies with international standard as elaborated by

Steffanoff et al. (1988) and is hereby presented in Figure 1.

Results of DPL testing are normally presented as a graph of number of blows against the

penetrated depth. Through such graphs, a change in soil layering may be depicted and number

of layers with their approximate thickness may be predicted over the penetrated depth. It has been

reported that DPL results may be influenced by deformation of driving rods, skin friction especially

in cohesive soils, driving rate and the application of driving energy. These effects may be

minimized by ensuring a vertical cone drive all the time, use of cone diameter slightly larger than

the rods diameter, a consistent driving rate normally of 15 to 30 blows/min as well as ensuring a

constant height of fall of the hammer.

2.5 General observations for data collected in-situ

Through practice and research, practitioners have documented important observations related to

application of in-situ tests for geotechnical investigations. This section summarizes information

relevant to the study.

2.5.1 Skin friction effect on DPL

In dynamic penetration testing such as with the DPL, the skin friction effect is greater in soft soils

(Steffanof et al., 1988). The test is considered more suitable for granular soils (Spagnoli, 2007).

However the effects may be reduced by using equipment with cone diameter significantly larger

than thickness of rods or using casings. According to Spagnoli (2007), cementation and relative

6

density of the soil considerably increase the recorded penetration resistance. In this study, the

soil was a dry stiff sandy, therefore the effects of skin friction are expected to be minimal.

Figure 1 Equipment used for in-situ testing (a) SPT (b) DPL (c) CPT

7

2.5.2 Effect of soil type on SPT results

Study by Bosscher and Showers (1987) indicates the effect of soil type on the amount of energy

losses during SPT operations with stiffer soils subject to higher losses which in turn, falsely

increases blow counts. Yokel (1989) studied the mechanism of energy transfer in SPT sampler

and concluded that the amount of energy actually used to penetrate the sampler depends on the

stiffness of soil such that it decreases with increase in number of blows. Lee et al. (2010) analysed

the reaction of SPT sampler as it strikes soils of different stiffness. They came to conclusion that

two different secondary impacts occur depending on soil penetration resistance where in soils

with 𝑁 < 25, additional sampler penetration is to be expected due to rebound impact while for

𝑁 > 50, the secondary impact does not contribute to further driving of the sampler hence larger

𝑁 values.

Typical side by side in-situ measurements from the study area are indicated in Figure 2 where the

high magnitudes of penetration resistance indicate a stiff to very stiff soil. Laboratory results

indicate the type of soil as sand with varying amounts of silt and clay. In the figure, it can be

observed that the gap between CPT and SPT profiles increase with depth. This may be explained

by the effect of soil stiffness to SPT values where falsely high 𝑁 values are recorded for stiffer

soils as the depth increases. The impact is an increased data scatter for the relationship between

𝑞𝑐 and 𝑁60. Since DPL resembles SPT in terms of both being dynamic methods, a similar effect

of soil stiffness to measured values is noted for 𝑁10 values as can be seen in Figure 2.

2.5.3 Effect of overburden stress on in-situ test results

In-situ measurements are affected by overburden stress at which they were determined. There

has been studies and suggestions on factors to account for overburden normalization in both SPT

(Liao and Whitman, 1986; Skempton, 1986) and CPT (Moss et al., 2006; Maki et al., 2013) among

others. According to Liao and Whitman (1986), the basis for the overburden correction factors rest

Figure 2 Side by side in-situ measurements at a location on the study area

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40 50 60 70 80

Dep

th (

m)

Measured soil Resistance

CPT qc (MPa) DPL N10 SPT N

8

on data for normally consolidated, uncemented, unaged, clean quartz sands. The suggested

corrections may therefore introduce errors if applied to mixed soils such as encountered in this

study site. Furthermore, overburden correction factors are not recommended for CPT

measurements taken at depths shallower than 20 m (Fellenius, 2009) and it was decided in this

study, not to correct the in-situ measurements before developing the relationships. After all, the

correlated pairs were basically recorded at the same depths and therefore are supposed to be

equally affected by stress levels. Some previously developed correlations between in-situ test

data such as those by Chin et al. (1990); Akca (2003); Bozbey and Togrol (2010) did also not

consider the overburden normalization of data pairs.

2.6 In-situ tests influence zones

When the SPT sampler is forced to penetrate through the ground, it influences in addition to the

penetrated 30 cm, a further distance equal to 4 to 7 times the sampler diameter (Rogers, 2006).

Similarly, the tip of an advancing 10 cm2 CPT cone is considered to influence a soil depth of about

38 cm ahead of it. In addition to sampler diameter, the size of the influence zone is also affected

by soil stiffness with deeper zones expected in stiffer soils. Study by Ahmadi and Robertson (2005)

indicated that the zone of influence in dense sand layers is about 10 – 20 times the cone diameter

for CPT. A similar condition is to be expected from an advancing DPL cone. In order to develop

correlations between in-situ test results, CPT and DPL data were averaged over a 560 cm depth

which is about 10 times the size of SPT sampler, being the largest of the three. This depth of

influence was decided taking into consideration the stiff to very stiff nature of the soil encountered

in the study site.

2.7 Previous correlations

The long term experience with the use of SPT and CPT for site characterization has enabled

development of many correlations between the test data and soil design parameters as well as

between data from the two test methods. This is not the case with DPL probably because the test

is only suitable for shallow investigations of about up to 10 m deep (Steffanoff et al., 1988).

Previous relationships between CPT and SPT data, example by Robertson et al. (1983) and

Anagnostopolous et al. (2003), were established on the ground of practitioners being well

experienced with SPT while the CPT was a new method that needed time to expertise. Other

reasons are for cross checking, comparison and evaluation of parameters obtained from the

correlated methods, to permit the use of interpretation methods or charts developed for one test

with the results of the other test and converting a database available for one test to a database

for the other test (Marchetti, 2011). Rogers (2006) recommends joint application of CPT and SPT

for better site investigation results.

2.7.1 CPT – DPL and SPT – DPL correlations

Generally, CPT – DPL and SPT – DPL are not common in literature. This may be a result of DPL

being a not so common method. Another probable factor is the fact that there exist several

dynamic probing equipment in use worldwide (Steffanoff et al., 1988) distinguished mainly by the

weight of the hammer that produces the driving energy, rod diameter and cone size. This means

existing correlations between dynamic probing data and other testing methods will differ

depending on the equipment used for data collection.

According to Figuiredo et al. (2013) research similar to the one presented in this thesis was

executed in Brazil to promote the use of DPL for design purposes. Their review revealed a good

agreement between CPT and DPL data which is attributed to geometrical resemblance of the

penetrometers. This study has also achieved similar findings where DPL data have been found to

9

better correlate to CPT than SPT data. The importance of local correlations is well acknowledged

by among others, Schmertmann (1978), on the basis that correlations may be significantly

different in different geological conditions. This calls for development of correlations suitable for

Dar es Salaam and eventually Tanzanian soils and make them available for local use. The

extensive use of SPT in Tanzania makes it of interest to develop correlations with both CPT and

DPL.

In an attempt to improve the correlation between SPT and CPT data, the components of cone

resistance and skin friction of CPT were added together. This is in line with Schmertmann (1979)

suggestion that SPT sampler is subjected to both tip resistance and sleeve friction during driving.

Unfortunately these two components are inseparable in the ordinary SPT procedure therefore the

alternative approach is to add the separately measured 𝑞𝑐 and 𝑓𝑠 prior to developing the

relationships. This approach resulted to a slightly better correlation between CPT and DPL data,

also CPT and SPT data in this study.

2.7.2 CPT – SPT correlations

Relationships between SPT and CPT data are very common in literature. A compilation can be

found in Akca (2003), who also noted the absence of geological description of the soils with

previously developed relationships. With application of arithmetic average and regression

analysis, he came out with relationships between SPT and CPT in carbonic soils of United Arab

Emirates. As a general observation, the correlations did not compare very well with those

suggested in previous literature. Most recently, Ahmed et al. (2014) produced correlations

applicable for both calcareous and siliceous soils in relation to compressibility characteristics of

the soil expressed in terms of 𝐷50 for SPT and soil behaviour index (𝐼𝑐) for CPT. The index 𝐼𝑐 is

obtained through equation 2.

The study by Chin et al. (1990) indicates two major observations for sandy soils; that the ratio 𝑞𝑐

𝑁⁄ decreases with fine contents and it correlates better with 𝐹% than 𝐷50. An important factor

to be noted from their study is that the tests were performed on hydraulically filled and natural

sand layers. Another factor noted from their study is that the energy correction to SPT was to 55%

and not the commonly suggested value of 60%. Edet et al. (1994) obtained strong correlation

between SPT and CPT data for costal sands which may be attributed to the few number of data

used. Elkateb and Ali (2010) ascertained the inapplicability of existing correlations for application

in fine to medium calcareous sandy soils. They also observed that the ratio 𝑞𝑐

𝑁⁄ for calcareous

sand is higher than for siliceous sands. Their study resulted to a modified relationship between

CPT and SPT that is based on 𝐼𝑐.

Jefferies and Davies (1993) aimed at providing a CPT – SPT relationship that may be applicable

without the need for soil sampling. From theoretical view, they urged that the ratio 𝑞𝑐

𝑁⁄ should

lie between 0.4 and 0.8. They proposed a correlation that is based on soil behaviour index 𝐼𝑐which

is basically a soil classification with CPT data, hence eliminated the necessity to sample the soil

to be able to relate SPT with CPT data.

𝐼𝑐 = √{3 − 𝑙𝑜𝑔[𝑄𝑛 (1 − 𝐵𝑞)]}2

+ {1.5 + 1.3(𝑙𝑜𝑔 𝐹𝑟)}2

𝐹𝑟 = 𝑓𝑠

𝑞𝑡 − 𝜎𝑣𝑜 × 100%

𝑄𝑛 = 𝑞𝑡 − 𝜎𝑣𝑜

𝜎𝑣𝑜´

𝐵𝑞 = 𝑢 − 𝑢𝑜

𝑞𝑡 − 𝜎𝑣𝑜

2

10

Kara and Gündüz (2010) applied arithmetic average and statistical regression analysis to

determine the relationship between CPT and SPT for heterogeneous soils of Turkey. The

arithmetic average method resulted to 𝑞𝑐

𝑁⁄ ratios similar to those previously obtained by other

researchers but the regression analysis method gave low coefficients of correlations which may

be attributed to the variability of the tested soils. Kasim et al. (1986) presented SPT – CPT

correlations in hydraulically placed sand fill underlain by natural sand layer. The results indicates

scatter of 𝑞𝑐

𝑁⁄ related to 𝐷50 especially for the natural sand which has higher fine content. The

approach by Kulhway and Mayne (1990) was to correlate the ratio 𝑞𝑐

𝑁⁄ with both 𝐷50 and 𝐹%

with a rather large database where they found out that the correlation with 𝐷50 was better than

that with 𝐹%, contrary to Chin et al. (1990). They extended the work done by Robertson et al.

(1983) by incorporating more data in their database.

Perhaps the most commonly referred CPT – SPT correlations are those developed by Robertson

et al. (1983) and their modification. The correlations expresses the relationship between 𝑞𝑐

𝑁⁄ and

𝐷50 with consideration of energy correction to measured 𝑁 values. They observed that the ratio

as well as the data scatter increases with increase in 𝐷50 which implies that SPT to CPT

correlations are expected to be poorer for soils with higher amounts of larger particles.

11

Chapter 3 – Soil modulus and its determination

3.1 General

Soil modulus is one of the most difficult soil parameters to estimate due to its dependency on so

many factors (Briaud, 2000). As such, the conditions associated with the soil modulus should be

reported with it whenever one wants to present the parameter. If a triaxial or oedometer test is

considered, a stress – strain curve may be plotted from the result of loading the soil sample. The

slope of the curve is related to the soil moduli in a convenient expression. Because soils do not

exhibit linear stress – strain relationships, many moduli may be defined from a stress – strain

curve such as secant, initial tangent, tangent and cyclic as elaborated in Figure 3. Regardless of

which slope is determined, the state at which the soil is at the time of determination of the modulus

will affect the determined modulus.

Duncan and Bursey (2013) identified the factors that affect determination of soil moduli. Briaud

(2000) discussed the factors under two headings; state factors and loading factors. He described

state factors as:

i Soil dry density – how close the particles are packed in the soil mass. High modulus is

expected for closely spaced soil particles.

ii Soil structure – how the soil particles are organized. Loose or dense for granular soils and

dispersed or flocculated for fine grained soils.

iii Water content of the soil – for fine grained soils, low water content may result to high soil

moduli such as dry clays whereas for coarse grained soils less lubrication is achieved between

particles which results to low density hence low moduli

iv Stress history of the soil – refers to stress at which the soil was subjected in the past.

Overconsolidated soils tend to have higher moduli than the normally consolidated deposits

because the former are in the reloading phase while the later are in the first cycle of loading.

v Cementation – may lead to significantly increased soil moduli. This may be temporal due to

water content or chemical cementation example due to presence of calcium particles between

soil particles.

Figure 3 Different types of soil moduli from a stress – strain curve

12

Loading related factors that influence soil moduli are identified as follows:

i The mean stress level of the soil – the confinement effect; the higher the stresses confining

the soil mass the higher the moduli.

ii Strain level in the soil – secant moduli depend on the mean strain level in the influence zone

where in most cases a decrease in soil moduli is expected for an increase in mean strain level

with few exceptions.

iii Strain rate in the soil – like other viscous materials behaviour, the faster the rate of loading the

stiffer the soil and therefore the higher the moduli appears to be.

iv The number of loading cycles experienced by the soil – if the loading is repeated several times,

the secant modulus tend to decrease with increase in loading cycles

v Drainage conditions – this refers to the time available for the soil to drain during loading. The

two extremes are undrained and drained conditions. The time required to maintain the

undrained condition or to ensure that complete drainage takes place depends on the soil type.

Depending on the condition, drained or undrained moduli may be determined.

3.2 Types of soil moduli

Soil moduli depend on stiffness. While the modulus is a soil property, stiffness is not a soil property

since it depends on the size of the loaded area (Briaud, 2000). This implies that for an elastic

material, the stiffness measured with one test will be different from the stiffness measured with

another test if the loading areas are different. However, the modulus obtained with each test will

be the same provided the state factors are the same.

The various types of soil moduli in relation to loading conditions are discussed by Duncan and

Bursey (2013) as:

i Young´s modulus (𝐸) is that determined by the ratio of change in axial stress to the change in

axial strain. This is defined for uniaxial loading conditions where the stress changes in only

one direction.

ii Shear modulus (𝐺) is the ratio of the change in shear stress to the change in shear strain for

pure shear loading.

iii Bulk modulus (𝐵) is the ratio of the change in the axial stress to the change in volumetric strain.

iv Constrained modulus (𝑀) is the ratio of change in axial stress to the change in axial strain for

condition where the strain in the horizontal direction is restricted

An important step in solving problems involving soil modulus is to clearly identify which modulus

is required for the analysis. This study is focused on constrained modulus obtained through

oedometer test as further discussed in section 3.3.

3.3 Determination of constrained modulus

Soil modulus is obtained by the ratio of change in applied stress to the change in respective strain.

For the loading condition where no strains are induced in the lateral direction, the determined

modulus is termed constrained modulus or one dimensional modulus, usually denoted by 𝑀. when

soil is axially loaded such as in a triaxial cell, the stress – strain curve plotted from the data is

normally non-liner. However, there are several ways of estimation the modulus from the non-linear

curve by considering the slope of a line through a point or a segment of the curve. Such procedure

result to one of the following moduli;

13

i The initial tangent modulus (𝑀𝑖) which is the slope of the stress – strain curve at the origin

ii The secant modulus (𝑀𝑠) which is the slope of a line between two points on stress – strain

curve

iii The tangent modulus (𝑀𝑡) which is the slope of stress – strain curve at some desired point

In this study, the secant constrained moduli were determined from plots of oedometer results

(such as one shown in Figure 4) for the stress increase from 100 to 200 kPa using the equation:

𝑀𝑠 = 𝛥𝜎´

𝛥𝑠 3

The common reference stress is 100 kPa e.g. Massarsch and Fellenius (2014) and the stress

increase between 100 and 200 kPa is the commonly considered in determination of soil moduli

for application in shallow footings (Briaud, 2000; Fransisca, 2007). The loading rate is very low

(from construction to many years of service) and the loading cycle is normally one.

3.4 Correlations with in-situ tests

Soil modulus may be obtained directly from laboratory test but often deemed inaccurate due to

sampling disturbance especially for granular soils. Moreover, oedometer test is costly and time

consuming. Correlations of soil modulus with laboratory or in-situ test data are alternative to the

seemingly inaccurate direct measurements. Correlations between in-situ test data and laboratory

obtained moduli are not very common in literature. The few existing are based on in-situ data

versus soil modulus back calculated from settlement actually recorded from built foundations such

as in D´Appolonia et al. (1968) and Shahien and Farouk (2013). However, such experiments are

costly and need long term involvement of the researcher to the respective projects which was not

possible for the time limited study presented here.

Figure 4 Stress – strain curve for oedometer data. Determination of 𝑀𝑠

0

0.02

0.04

0.06

0.08

0.1

0.12

1 10 100 1000

Str

ain

s'

Normal stress in kN/m2

14

The tangent constrained modulus obtained from one dimensional compression test has been

correlated with CPT. Kulhway and Mayne (1990) reports the general form of correlation as:

𝑀 = 𝛼𝑞𝑐 4

With values of 𝛼 related to the relative density of sand in calibration chamber studies and range

from 3 to 8 for normally consolidated sands and between 0.4 and 8 for cohesive soils. The

conditions for sands are drained tangential modulus while for cohesive soil, the reported values

are for drained secant moduli.

The constrained modulus for one dimensional compression test in clays has been correlated with

SPT 𝑁 values. Relationships are of the form presented by equation 5:

𝑀 = 𝑓𝑁 5

With 𝑓 related to 𝑃𝐼 of the soil. However, Kulhway and Mayne (1990) report such correlations to

be weak. A relationship between 𝑁 and 𝑀𝑠 from saturated and unsaturated soil is also found in

Fransisca (2007) where an exponential relationship was proposed between the data.

Probably the best in-situ test for determining constrained modulus is the dilatometer test. Study

by Iwasaki et al. (1991) indicated a good agreement between oedometer and dilatometer

constrained modulus for alluvial soils and this is particularly due to the nature of the in-situ test

itself being different from CPT or SPT (Marchetti, 2011).

15

Chapter 4 – Geotechnical uncertainties and their determination

5.1 Sources of uncertainties

Uncertainties in geotechnical engineering are a contribution from three major sources (Phoon et

al., 1995, Phoon and Kulhawy, 1999; Baker and Calle, 2006, Ching et al., 2010); natural inherent

variability, measurement errors and transformation uncertainties. The natural inherent variability

of a soil parameter is caused by the geological process of soil formation. Studies such as by Zhang

et al. (2008) indicate that even homogeneous soils in centrifuge tests may have significant

variability. Measurement error originate from systematic and random errors arising during testing,

including equipment errors, procedural - operator errors and random testing effects.

Transformation uncertainty are induced in the process of evaluating design parameters from

measured in-situ or laboratory values due to the uncertainty in the theoretical and empirical

transformation models. The importance of separating the components of uncertainties during

evaluation is explained by Phoon et al. (1995) as to allow their application in a wider general

conditions rather than being project specific.

As compared to other forms of uncertainty, transformation uncertainty has not been extensively

investigated and therefore needs attention (Uzielli and Mayne, 2013). Figure 5 elaborates the

determination of transformation model uncertainty from a regression analysis as stipulated by

Phoon et al. (1995). In the analysis, the magnitude of the transformation error is represented by

standard deviation (𝑠𝜀) of the scatter (𝜀) around the model.

Normally, measurement errors are expected to be smaller than soil´s natural variability (Wu, 2013)

except for some special cases. A study by Akbas and Kulhawy (2010) revealed that the variability

calculated for directly measured parameters are significantly less than those derived from

correlations. Field tests as well as tests susceptible to sample disturbance are expected to have

large uncertainties (Ching et al., 2013).

Figure 5 Probabilistic characterization of transformation model (Phoon et al. 1995)

16

5.2 Evaluation of uncertainties

The observed soil property variability in spatial dimension suggests the resemblance to random

fields. Study by Baker (1984) gives an insight to modelling soil variability stochastically as random

fields. In this concept, the actual value of a soil property at each location within the unit is assumed

to be a realisation of a random variable. Nevertheless, it is important to note that the variation of

soil properties from one location to another is not random and properties at every location could

be known through testing. However, it is practically impossible to undertake such a volume of

investigation making it convenient to model spatial variation as random (Baecher, 1982). The two

parameters used to describe a random field are the coefficient of variation (𝐶𝑂𝑉) and the scale of

fluctuation (𝜃).

Application of random field theory require samples to be independent of their location. If this

condition is satisfied, data are said to be stationary. As described by Baker and Calle (2006),

stationarity (or homogeneity) in a strict sense means that the entire joint probability density

function of soil property values at an arbitrary number of locations within the soil unit is invariable.

A more relaxed criterion is that expected mean value and variance of the soil property is constant

throughout the soil unit and that the covariance of the soil property values at two locations is a

function of the separation distance between the locations only. Random fields satisfying only the

relaxed criteria are called stationary in a weak sense.

There are a number of methods available to assess stationarity of a data set, including

examination of histogram plots and Kendall´s Tau test. Removing trends with methods such as

regression analysis from original data modifies non stationary to stationary data (Campanella et

al. 1987). In the process, a line or curve of best fit is estimated with ordinary least squares and

then subtracted from the data. The residuals are then used for further analysis with random fields.

The type of trend removed has been found by Cafaro and Cherubini (2002) to affect the evaluated

uncertainty as they obtained different vertical scale of fluctuation respect to CPT data with

residues after quadratic and linear trend removal. The distinction between trend and stochastic

component is the modeller’s choice (Baecher, 1999) and the trends should be kept simple.

5.3 Variance reduction

The continuity and heterogeneity of soil mass supporting a foundation controls the performance

of the foundation making spatial variability of geotechnical performance of a structure be of

importance to determine. This and the fact that geotechnical parameters vary from site to site as

well as from layer to layer are the two major aspects that differentiate geotechnical reliability

analysis from structural reliability analysis (Honjo and Otake, 2013). Soil properties are rarely

modelled as particle properties. As such, all engineering characteristics of soils are properties of

a local average of a kind. Griffiths and Fenton (2007) identified the two main effects of local

averaging as to reduce the variance and to lessen the effect of contribution from the components

with high frequency. Vanmarcke (1977) proposed a method of reducing the variance of a local

average from the variance of a sampled random field by a pre-determined factor which depends

on the size of the local average and the scale of fluctuation.

The scale of fluctuation (𝜃) is defined as the distance within which soil property shows persistence

from point to point. Small values of 𝜃 implies a rapid variation about the mean. Several methods

are available for determination 𝜃 including use of autocorrelation functions, use of variograms or

the approximate method proposed by Vanmarcke (1977). Some researchers have reported the

dependence of 𝜃 on sampling domain (Fenton, 1999; Cafaro and Cherubini, 2002; Jones et al.,

2002) with larger values related to wider sampling intervals. Apart from the application in

determining variance reduction, 𝜃 values may be interpreted as the optimum sampling interval of

a given test method (Campanella et al. 1987).

17

The variance of an averaged soil property over a surface or volume is likely to be substantially

less than the field variance, which is mainly based on small sample tests or small affected volumes

in in-situ tests. In a known size of the failure domain, the variance of the average value is obtained

by reducing the variance of the measured parameter. Such a reduction can be mathematically

modelled using the random field model of Vanmarcke (1977), and can be expressed as:

𝑉𝑎𝑟(�̅�) = 𝛤2𝑉𝑎𝑟(𝑋) 6

where, 𝑋 is a random variable with the mean �̅�, 𝑉𝑎𝑟(∙) denotes the variance of a random variable,

and Γ2 is referred to as the variance reduction factor. The evaluation of Γ2 is in general

complicated. However, Vanmarcke (1977) proposed approximate solution presented as equation

7 as:

Γ2 =

𝜃

𝐿 for 𝐿 > 𝜃

Γ2 = 1.0 for 𝐿 ≤ 𝜃

7

where 𝐿 is the size of the failure domain.

5.4 Importance of quantifying uncertainties

The field of geotechnical engineering faces more uncertainty than any other field in civil

engineering (Bilgin and Mansour, 2013). In such situations, the application of reliability based

design becomes more beneficial than deterministic methods. In response, numerous studies have

been performed recently in the area of uncertainties and reliability based design. Assessment of

spatial variability of soils requires a very large amount of closely spaced and accurate data (Jaksa,

2013) which makes the CPT ideal for such purposes as it yields a large number of closely spaced

data within a short time and a small effort as compared to other tests such as the SPT. For this

reason, many studies have been performed in relation to CPT. It is high time to involve data from

other types of soil investigation methods in uncertainty studies to allow their application in reliability

based design problems. Phoon and Kulhway (1999) and Jones et al. (2002) reported that the

amount of information on scale of fluctuation of geotechnical parameter is limited in comparison

to the information on coefficient of variation. This observation is still valid today and more studies

should be conducted to fill this gape.

As stipulated by Phoon and Kulhawy (1999), the contribution to total variability of a design

parameter depends on the site conditions, degree of equipment and procedural control during

testing, and quality of the transformation model. In this particular study, the three in-situ methods

considered were able to predict the constrained modulus with similar magnitudes of total

variability. Data applied were from the same site hence same site conditions, a rather high degree

of control was exercised during testing with both methods and the same crew was involved.

Transformation models considered in this study were developed with data from the same site.

This explains the similar magnitude of total variability obtained in association with the methods.

18

Chapter 5 – Consequences of uncertainties

5.1 Importance of evaluating the consequences of uncertainties

Uncertainties in a designed system are directly related to the anticipated risks such that higher

uncertain components imply higher probability of occurrence of adverse effects. With proper

consideration of uncertainties, the safety of structures and hence their economy may be

evaluated. The analysis of safety is crucial to any design because too low safety standards may

result to losses of property and lives while too high safety standards results to overly expensive

systems. In the context of the current research, evaluated consequences of uncertainties are

intended for comparing effectiveness of different soil investigation methods.

Four different soil investigation methods have been applied to gather data for this research where

uncertainties have been quantified in association to each method. For the in-situ methods, the

uncertainties obtained are of similar order of magnitudes and different from those of laboratory

method. No conclusion can be drawn about the effectiveness of each method without determining

the effect that the uncertainties have to a designed system. The approach which will be adopted

in this study is to perform designs which incorporate the uncertainties and compare the reliability

instead of the uncertainties. Probabilistic design methods allow for inclusion of uncertainties and

therefore render themselves as perfect tools for evaluating the consequences.

5.2 Computation of failure probability

A successfully designed system must meet the two requirements of safety and economy. The

two extremes of an improper design are the economically unacceptable design and the failed

design. Taking the case of design of a shallow foundation as an example, an uneconomic design

would be when the provided size of the foundation is unnecessarily too big for the loads intended

to be carried and a failed foundation may be that which has settled in excess of the allowable

settlements. In this context, failure does not necessarily be catastrophic such as the collapse of

the building but is defined as performing below the acceptable standards.

The general definition of foundation failure is when the load (𝑄) that has to be supported, transmit

to the soil stresses higher than what the resistance (𝑅) is capable of offering. In other words,

failure is when 𝑄 > 𝑅 and the probability of failure (𝑝𝑓) is given by

𝑝𝑓 = 𝑒𝑣𝑒𝑛𝑡𝑠 𝑡ℎ𝑎𝑡 𝑄 > 𝑅

𝑡𝑜𝑡𝑎𝑙 𝑒𝑣𝑒𝑛𝑡𝑠 8

A robust and straightforward technique for obtaining the events in equation 8 and eventually

calculating 𝑝𝑓 is the Monte Carlo simulation method based on randomized input.

Through repeated execution of an existing deterministic process, Monte Carlo simulation method

offers the simulation of possible scenarios on an investigated effect, such as settlement values of

a footing according to the probability distributions of the random variables involved, and then infer

the probability of various events from the observed outcomes of all simulation runs. By setting a

desired limit, output variables may be divided into two sets representing success and failure,

hence the probability of failure may be calculated. The accuracy of Monte Carlo simulation results

depends on the number of performed simulations and the expected probability of failure. When

the probability of failure is very small, the number of simulations required to obtain an accurate

result becomes very large. According to Phoon (2008, p 6), the rule of thumb is to have number

of simulations 𝑛 = 10𝑝𝑓

⁄ to estimate 𝑝𝑓 within a 𝐶𝑂𝑉 of 0.30. But 𝑝𝑓 values cannot be known

before hand and therefore may be represented by some typical values, �̂�𝑓. For geotechnical

19

design problems, �̂�𝑓 values are usually smaller than 0.001 which implies that 𝑛 should be in order

of 10,000. A more general method of determining the minimum number of required simulation is

provided by Griffiths and Fenton (2007, p 18) as follows;

𝑛 = �̂�𝑓(1 − �̂�𝑓)

𝑆𝐷𝑝𝑓

2 9

where 𝑆𝐷�̂�𝑓

2 is the variance of the estimated �̂�𝑓

It is common to express reliability in the form of reliability index which is related to 𝑝𝑓. Both 𝑄 and

𝑅 are uncertain quantities, therefore the variables have means and variances. According to

Baecher and Christian (2003, p 304), a reliability index (𝛽) is defined in terms of the safety margin

(𝑆𝑀) according to equation 10 and it expresses the distance of the mean margin from its critical

value in units of standard deviation.

𝛽 = 𝜇𝑆𝑀

𝑆𝐷𝑆𝑀 10

in which 𝜇𝑆𝑀 and 𝑆𝐷𝑆𝑀 are the mean and standard deviation respectively for the margin of safety

which is obtained by the difference between 𝑅 and 𝑄 as expressed in equation 11.

𝑆𝑀 = 𝑅 − 𝑄 11

When 𝑅 and 𝑄 are normally distributed, 𝑆𝑀 is also normally distributed which makes 𝛽 a standard

normal variate (Baecher and Christian, 2003, p 305). In such case, 𝛽 and 𝑝𝑓 are related by

equation 12 as;

𝛽 = −Φ−1(𝑝𝑓) 12

in which Φ−1(∙) is the inverse standard normal cumulative function.

5.3 Input to the performance function

The traditional approach to dealing with uncertainties in geotechnical engineering is to express

the margin of safety in terms of a factor of safety (𝐹𝑠) as follows;

𝐹𝑠 =𝑅

𝑄 13

In foundation design problems for example, a global factor of safety usually between 2 and 3 is

applied to the resistance. Either 𝑆𝑀 in equation 11 or 𝐹𝑠 in equation 13 can describe the

performance of a geotechnical structure and they are called performance functions. Both 𝑅 and 𝑄

must be taken in broad definition that includes not only forces and stresses but also other

phenomena that may need to be considered in design such as, in this study, settlement.

For typical structures with isolated spread footings, a total foundation settlement of 25 mm is a

common design value resulting in acceptable differential settlements. The allowable load is then

defined as the load resulting in 25 mm of total settlement and may be considered as 𝑅 in equations

11 and 13. The variable 𝑄 will be the design load of the respective foundation. The problem can

be simplified by considering settlements instead of loads as inputs to equations 11 and 13. In this

case, 𝑅 will be the limit settlement of 25 mm and 𝑄 the calculated foundation settlement.

In the current study, the major input to the performance function is the settlements which may be

predicted by a number of existing methods in literature. Three methods have been chosen to

evaluate elastic settlements based on availability of data. The first method is that proposed by

20

D´Appolonia et al. (1968) which allows the use of soils´ constrained modulus. The second method

is that introduced by Schmertmann (1970) and later modified by Schmertmann et al. (1978). This

semi empirical method is intended for application of in-situ data, especially the CPT. The third

method that shall be considered is that developed by Burland and Burbidge (1985). The method

is one of the most comprehensive efforts in the area of in-situ methods application which basically

uses SPT data. Details and procedures of conducting the methods are not considered at this

stage.

5.4 Comparing probabilities of failure

Reliability indices for most geotechnical designs lie between 1 and 5, corresponding to

probabilities of failure ranging from about 0.16 to 3 × 10−7 (Phoon, 2008) as shown in Figure 6.

The figure may conveniently be used to compare results from alternative design and recommend

the best alternative among comparisons. However, when comparing results at a close range, say

both being in the range of `poor´ and `below average´ as indicated in Figure 6, the comparison

becomes not so elaborative to assist a proper recommendation. Expressing 𝛽 or 𝑝𝑓 in terms of

𝐹𝑠 may help to provide custom values which are readily comparable and understandable among

practitioners. It will also allow comparison between probabilistic and deterministic design outputs.

According to Baecher and Christian (2003, p 306), 𝛽 and 𝐹𝑠 are related by equation 14 as follows;

β =𝐸[𝐹𝑠] − 1

𝑆𝐷𝐹𝑠

14

in which 𝐸[𝐹𝑠] is the expected factor of safety and 𝑆𝐷𝐹𝑠 its standard deviation.

Figure 6 Relationship between 𝛽 and 𝑝𝑓 (Phoon, 2008 p 29). Classification proposed by

U.S. Army Corps of Engineers (1997)

21

Chapter 6 – Summary of appended papers

This chapter provides a summary of papers that form the licentiate thesis.

6.1 Paper I

Correlations of SPT, CPT and DPL data for sandy soil in Tanzania

Mwajuma Ibrahim Lingwanda, Stefan Larsson and Dalmas L. Nyaoro

Submitted to Geotechnical and Geological Engineering in April 2014

This paper aims at extending the use of DPL data to analysis and design rather than just for site

stratification in Tanzania. Both being common in-situ methods around the world, there exist many

studies that empirically relate CPT and SPT data to soil design values. Unfortunately, the same

cannot be said to DPL hence limiting its application to mainly soil stratification. Correlations were

established between SPT, CPT and DPL data obtained from a research oriented site investigation

in a sandy soil. The type of geology where the data were collected dominates a significant portion

of Dar es Salaam city in Tanzania. The study is based on side by side data from 8 SPT boreholes,

8 CPT soundings and 8 DPL soundings conducted on a 30 m2 area. The distance between side

by side measurements is kept at a small radius of 0.5 m to minimize the effects of soil variability

to the correlations. Two methods were implemented in the process of establishing relationship

between the in-situ methods; the arithmetic average method and the linear regression method.

To improve the relationships between data, outliers were detected using the Tukey mean –

difference plots and filtered from the data sets. There is also a slight improvement of the

relationships when the cone resistance and sleeve friction components of soil resistance are

added together for establishing correlations between CPT and data from the other two in-situ

methods used in this study. The arithmetic mean method gave the following expressions;

𝑞𝑐𝑁60

⁄ = 0.37, (𝑞𝑐 + 𝑓𝑠)

𝑁60⁄ = 0.46 and

𝑁60𝑁10

⁄ ≈ 1. Through the linear regression method, the

following relationships have been obtained; 𝑞𝑐 = 0.15𝑁60 + 7.49, 𝑞𝑐 = 0.38𝑁10 + 1.57 and 𝑁60 =

1.01𝑁10 + 0.44. By examining the coefficients of correlation and the transformation uncertainties,

it was revealed that DPL data correlate with CPT data better than with SPT data which leads to

the suggestion that DPL data should be transformed to equivalent CPT rather than SPT when

such information is to be used for geotechnical analysis and design. Although CPT – SPT

correlations are common in literature, local correlations were established in this study and

compared to those existing in literature where they seem to be fairly comparable.

6.2 Paper II

Inherent soil variability linked to different characterization methods

Mwajuma Ibrahim Lingwanda, Stefan Larsson and Dalmas L. Nyaoro

Presented to Sida Annual Regional Conference, RegConf 2014(050) in July 2014

Evaluation of geotechnical uncertainties has been a subject of interest to the geotechnical

community where several studies have been performed recently under different conditions. This

study is limited to evaluation of inherent soil variability of a stiff sandy soil where three in-situ and

one laboratory method are involved in measuring soil response to loading. Actual field and lab

data were employed from a site investigation program where 8 CPT soundings, 8 DPL soundings,

8 SPT profiles and oedometer test of samples from 8 boreholes were involved in the analysis.

22

From the data, coefficient of variation of inherent soil variability was evaluated from each test

method. Trends were first removed from the original data to achieve weak stationarity condition

and the residue was further analysed to determine the standard deviation which was used to

determine coefficients of variation. In average the results indicate minimum variability from

laboratory oedometer test at average 𝐶𝑂𝑉 = 0.24, DPL and CPT are close at average 𝐶𝑂𝑉 = 0.32

and 𝐶𝑂𝑉 = 0.33 respectivelly. The SPT resulted to the highest variability of 𝐶𝑂𝑉 = 0.41 in

average. An important note is that in this study, due to the difficulty involved, measurement errors

were not separated from the inherent soil variability thus limiting the application of study findings.

However, the study indicates that DPL data can be trusted for design use just as the common

CPT and SPT due to similar magnitudes of total variability associated with the methods.

6.3 Paper III

Comparison of geotechnical uncertainties linked to different soil characterization

methods

Mwajuma Ibrahim Lingwanda, Anders Prästings, Stefan Larsson and Dalmas L. Nyaoro

Submitted to Geomechanics and Geoengineering: An International Journal in September 2014

In this paper, total uncertainties in determining soil constrained modulus in relation to CPT, DPL,

SPT and oedometer tests was evaluated and compared. Separate determination of inherent soil

variability and transformation uncertainties were conducted and summed. Measurement errors

were not separated from data used. The two random field parameters, the coefficient of variation

and scale of fluctuation were evaluated in horizontal and vertical directions. Results from different

methods of evaluating scale of fluctuation were also compared. Study data includes 29 CPT

soundings, 8 DPL soundings, 8 SPT profiles and 36 laboratory oedometer tests of samples from

8 boreholes. In order to demonstrate magnitudes of transformation errors, empirical correlations

were first established between the in-situ test data and the secant constrained moduli from

oedometer test as 𝑀𝑠 = 0.25𝑞𝑐 + 2.26 where 𝐶𝑂𝑉𝑡𝑟𝑎𝑛𝑠 = 0.28, 𝑀𝑠 = 0.14𝑁10 + 1.07 with

𝐶𝑂𝑉𝑡𝑟𝑎𝑛𝑠 = 0.26 and 𝑀𝑠 = 0.06𝑁60 + 3.04 with 𝐶𝑂𝑉𝑡𝑟𝑎𝑛𝑠 = 0.28. The total uncertainties for

determination of constrained modulus were found to be minimum for the direct measured values

with oedometer at 𝐶𝑂𝑉 = 0.24, CPT and DPL data resulted to similar magnitudes of total

uncertainties at 𝐶𝑂𝑉 = 0.46 and 0.42 respectively. SPT data resulted to the highest total

uncertainties at 𝐶𝑂𝑉 = 0.51. Using the simple approximate method for determination of scale of

fluctuation, 𝜃𝑣 = 3.3 𝑚 and 2.7 𝑚 in average for SPT and oedometer data respectively. For CPT

and DPL data, 𝜃𝑣 = 1.1 𝑚 and 1.0 𝑚 respectively by using the method of Bartlett’s limits. The

horizontal scale of fluctuation was also determined respect to each method. The general

observation with regard to vertical and horizontal scales of fluctuation is that the magnitudes

depend on interval of data measurement and that similar magnitudes of 𝜃𝑣 and 𝜃ℎ are to be

expected from the simple and sophisticated methods of calculations. This suggests that in case

of data limitations, reliable scale of fluctuation may be inferred from limited samples using the

simple approximate method.

23

Chapter 7 – Conclusions and recommendations

In many geotechnical studies, soils are grouped into two broad categories of clay and sands. The

study of intermediate soils also termed as non- text book soils (Mayne, 2006) is demanded. This

study was performed on clayey sand to silty sand soil in Tanzania. The studied soil dominates a

significant portion of the west part of Dar es Salaam city therefore the results may benefit much

of the area. Through the study presented in this thesis, the following have been achieved:

i Correlations between in-situ test data

Correlations have been established between SPT and DPL, SPT and CPT as well as between

CPT and DPL data where it was established that DPL – CPT correlation is better than DPL – SPT

hence the former is recommended for intermediate transformation of DPL data to design values.

Application of such transformation will extend the use of DPL data from soil stratification to

analysis and design of geotechnical structures especially shallow foundations. SPT – CPT

correlations are common in literature. However, this study has established correlations specific

for stiff, dry, clayey to silty sands. The correlations appear to agree with those proposed in

literature with slight differences. Researchers, e.g. Akbas and Kulhawy (2010) agree on

preference of local correlations over globalized ones. Ching and Phoon (2012) observed that site-

specific models are generally more precise than global models, although they can be significantly

biased when applied to another site. To avoid this bias, the developed correlations should be

applied with caution. In a wider picture, the correlations developed in this study are a framework

for future refinement.

ii Correlations between oedometer data an in-situ data

Within this limited data base, correlations have been established between in-situ tests (SPT, CPT

and DPL) and constrained modulus from oedometer test. These relationships have been found to

have similar data scatter and therefore similar transformation errors. This may mean that the tests

can predict the modulus with similar uncertainties. Considering that in-situ tests are far less

expensive as compared to laboratory methods, for example Nilsson (2013) reports a cost

comparison of one triaxial test equivalent to ten DPL tests, the correlations developed in this study,

if practically implemented may result to a significant reduction of the cost of geotechnical

investigation works in the Dar es Salaam and areas of similar geology.

iii Evaluation of geotechnical uncertainties

Natural inherent soil variability and transformation uncertainties were evaluated in relation to SPT,

CPT, DPL and oedometer tests. The total uncertainty was determined relative to each method

where it was revealed that SPT had the highest uncertainties although not far from CPT and DPL.

The oedometer test was associated to the least uncertainties in comparison to the in-situ tests.

The similar total uncertainty gives hope that even less developed methods such as the DPL are

capable of producing a good repeatability if they are carefully performed. Just how significant is

the difference in uncertainties evaluated with each method remains a question for further research.

A comparison of results from simple methods and sophisticated methods for determination of

scale of fluctuation revealed a consistence in the methods. This observation is also reported by

Vessia and Cherubini (2007) who obtained close results for scale of fluctuation determined by

Vanmarcke (1977) method and from autocorrelation method in a sandy deposit. This is important

for promoting the use of RBD in geotechnical problems because simplified methods are more

attractive to users.

The information obtained through this study may be applicable for projects under similar geologic

conditions or as prior information on a Bayesian updating type of analysis. The overall

achievement is that this study may lead to a more cost effective design of foundations.

24

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Appended Papers