Density Effects on
Tailings Behaviour
A Laboratory Study on Geotechnical Properties
Viktor Wiklund
Civilingenjör, Väg- och vattenbyggnad 2018
Luleå tekniska universitet
I PREFACE
This master thesis is the final part of my Master of Science in Civil Engineering, with speciali-zation in mining and geotechnical engineering. In the last 5 months at Luleå University of Tech-nology, I have worked with this thesis and studied the fines content and density effects on the material behaviour of tailings.
I would first like to thank my supervisor Roger Knutsson and my examiner Professor Jan Laue, at Luleå University of Technology, for all guidance and discussions regarding the work.
Furthermore, I also would like to thank both LKAB and TCS for provided materials and infor-mation, and also meaningful discussions regarding the work.
Lastly, I would like to show my gratitude to family, friends and classmates for all support during my time as a student.
Viktor Wiklund
II ABSTRACT
Tailings are a rest product from the extraction of metals and minerals, and is therefore produced in large volumes by all mining companies. One common way to store tailings material is to deposit it as a hydraulic slurry on a tailings impoundment, where the tailings are held in place by tailings dams. Deposit and discharge of tailings, often conducted along the dams, causes a particle segregation which creates different fines contents (percentage of particles smaller than 0,063 mm in the tailings) in the impoundment at various distances from the discharge. Another effect from the discharge is that different densities are created in the deposited layers. Since some tailings dams are constructed on top of old deposited tailings, and if possible with tailings as a construc-tion material, the fines content and density effects on the tailings behaviour are important factors for dam stability.
In this thesis, tailings material with different fines contents and different densities have been studied with the purpose to see how the behaviour in strength, compressibility and permeability varies. After an initial case study of sampled tailings from a specific impoundment, the fines content for the three tested materials were determined to be 10, 50 respectively 90%.
The behaviour in strength was tested in both triaxial and simple shear tests. Only drained strength was studied for three consolidation stresses in both apparatuses. The result from both tests showed that the strength is increasing with decreasing fines content, and thus evaluated friction angles increases with decreasing fines content. Evaluated friction angles from the simple shear test are though significantly smaller than those from the triaxial tests. Friction angles from triaxial tests are seen as most reliable, since the principal stresses are controlled during the whole test. The difference in friction angles from simple shear and triaxial test is however not a new discovery, it has been found by others before. The results from the triaxial tests indicates that a transitional fines content must exist somewhere between 10 – 50 %, where the behaviour in strength switches from sand dominated to silt dominated.
Oedometer tests were conducted to study the compressibility of the three materials. The results showed that the compressibility increased with increasing fines content and with decreased den-sity. In agreement with that conclusion, evaluated oedometer modulus from the normal consol-idation curve tended to increase with increasing density and to a smaller extent increase with decreasing fines content.
Determination of characteristics in permeability were done by evaluating the hydraulic conduc-tivity from constant head tests. Results from this showed that the hydraulic conducconduc-tivity increases with decreasing fines content. Furthermore, with increasing density the hydraulic conductivity decreases.
III
SAMMANFATTNING
Anrikningssand (eng. tailings) är en restprodukt från utvinningen av metaller och mineraler. Alla gruvföretag producerar varje år stora volymer anrikningssand som måste förvaras på något sätt. Detta görs ofta genom att anrikningssanden deponeras som en slurry med processvatten på ma-gasin. Anrikningssanden hålls sedan på plats av dammar och ibland i kombination med naturlig topografi. Deponeringen sker ofta från utsläppspunkter längs dammen, vilket resulterar i en sor-tering av kornstorlekar i magasinet som i sin tur skapar olika finjordshalter (procent av partiklar mindre än 0,063mm) på olika avstånd från utsläppspunkten. Deponeringen skapar också olika lager, som också får olika densiteter. Eftersom en del typer av gruvdammar byggs inåt och grund-läggs på tidigare deponerad anrikningssand, samt eftersom anrikningssand ibland används som byggmaterial vid höjningar, är finjordshalten och densitetens effekt på materialbeteendet intres-sant ur stabilitetssynpunkt för dammarna.
I det här arbetet har anrikningssand med olika finjordshalter och densiteter undersökts i labora-torieförsök för att bestämma hållfasthets-, kompressions- och permeabilitetsegenskaper. Först gjordes en case study, med provtagning och klassificering av anrikningssand från en specifik an-läggning. Därefter bestämdes att tre stycken material med finjordshalter på 10, 50 och 90 % skulle undersökas.
Hållfasthetsegenskaper har undersökts i både triaxial och direkta skjuvförsök. Endast dränerad hållfasthet har studerats för tre stycken konsolideringsspänningar för varje material i både triaxial och direkta skjuvförsök. Resultaten från både triaxialförsök och direkta skjuvförsök visar att håll-fastheten ökar med minskad finjordshalt och därför ökar även värdet på utvärderade friktions-vinklar med minskad finjordshalt. Utvärderade friktionsfriktions-vinklar från direkta skjuvförsök är dock betydligt lägre än friktionsvinklar från triaxialförsök. Friktionsvinklarna från triaxialförsöken är mer trovärdiga eftersom man under hela testet har koll på huvudspänningsriktningarna. Skillna-den i resultatet mellan direkta skjuvförsök och triaxialförsök är inte en ny upptäckt, utan har hittats av andra tidigare. Från resultatet av triaxialförsöken i det här arbetet kan man antyda att det finns ett ”transitional fines content” (TFC) mellan 10 och 50 %, där materialet övergår från sand dominerat beteende till silt dominerat beteende under skjuvning.
Ödometerförsök utfördes för att studera kompressionen hos de tre materialen. Resultaten visar att kompressibiliteten ökar med ökad finjordshalt och med lägre densitet. Utvärderade ödometer moduler från normalkonsolideringskurvorna visar att styvheten ökar med ökad densitet, samt en aning till tendens mellan ökad styvhet och minskad finjordshalt.
Permeabilitetsegenskaper har studerats genom utvärdering av hydraulisk konduktivitet från con-stant head test. Det observerades att den hydrauliska konduktiviteten ökar med minskad finjords-halt. Gällande densitetens effekt visar resultaten att med ökad densitet så minskar den hydrauliska konduktiviteten.
IV
TABLE OF CONTENT
1 INTRODUCTION ...1
1.1 Background ...1
1.2 Aim and objective ...5
1.3 Delimitations ...5
2 SELECTION OF MATERIALS ...6
2.1 Case study – Kiruna Tailings ...6
2.2 Sampling and geotechnical classification ...6
2.3 Material selection ... 12
2.3.1 Span of fines content (FC) ... 12
2.3.2 Span of densities ... 13
3 LABORATORY STUDY ... 15
3.1 Mechanical behaviour ... 15
3.2 Triaxial test ... 19
3.3 Simple shear test ... 23
3.4 Oedometer test ... 25
3.5 Hydraulic behaviour ... 26
4 RESULTS ... 29
4.1 Mechanical behaviour ... 29
4.1.1 Triaxial tests ... 29
4.1.2 Simple shear tests ... 33
4.1.3 Oedometer tests ... 36
4.2 Hydraulic behaviour ... 37
4.2.1 Constant head tests ... 37
4.3 Empirical relations – Fines content and density effects ... 39
5 DISCUSSION ... 41
6 CONCLUSIONS ... 44
6.1 Future work ... 44
1
1
INTRODUCTION
1.1
Background
Tailings and tailings dams
Tailings are a crushed and grinded mine waste material that remains after extraction of desired metals and minerals. The particle sizes of tailings are in general in the fractions of sand and silt, although in different amounts based on the origin of the ore and the extraction process. In most extraction processes a lot of water is used, and hence the final rest product becomes a slurry of tailings and water. After a de-watering stage the slurry is transported to a tailings storage facility, which commonly is in the form of a tailings impoundment. At the impoundment the tailings are deposit and held in place by tailings dams and if possible, in combination with natural topog-raphy (Vick, 1990).
The largest difference between a tailings dam and a water retention dam is that a tailings dam is usually continuously constructed, with so called raised embankments. With raised embankments, each raise is conducted by adding a new dyke in connection with the already existing embank-ment. Hence the embankment is continuously raised in suitable stages, in agreement with the pace that tailings are produced (Vick, 1990). Furthermore, a gradually raised tailings dam can be categorized in mainly three ways, based on which method used during construction. The three methods are the upstream, downstream and centreline method (Vick, 1990). Since the methods have different advantages and disadvantages, they are also suitable at different sites and for differ-ent conditions.
With the upstream construction method, the embankment is continuously raised upstream, i.e. inwards against the centre of the impoundment. The upstream construction method is under right circumstances known for its simplicity, regarding both construction techniques and costs. Downstream and centreline constructed dams are completely respectively partially growing out-wards, making it easier to construct stable dams but with the disadvantage of higher costs and handling of larger volumes of embankment material (Vick, 1990). For upstream (and to a small extent centreline) constructed dams the impoundment itself will be a part of the dam. This is a consequence of the fact that the dams grow inwards, and each new dyke will partially be con-structed on top of previously deposited layers of tailings (Bjelkevik, 2005). Regardless construc-tion type, the tailings itself can be used as construcconstruc-tion material for the new dykes. For the downstream and centreline embankments it is not always possible to solely rely on tailings, since the pace that tailings are produced are not high enough. For upstream constructed dams it is possible to directly move and compact the tailings closest to the crest to construct the new dyke, provided that the characteristics of the tailings are good (Vick, 1990).
Discharge and deposition
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particles in beach. Theoretically, due to the immediately loss of kinetic energy when the slurry is discharged the coarser particles will settle close to the discharge while the finer particles are suspended for a longer time and settles further away from the discharge (Blight, 2001). Some of the finest particles finally settles in standing water at the pond, in the lowest part of the impound-ment (Vick, 1990).
The particle size segregation will in other words control the particle size distribution along the whole beach, but also partly control it with depth since with time the elevation of the impound-ment surface is increasing. The fines content, FC, is the percentage of particles smaller than 0,063mm and it is an effective measure of the particle size distribution, since it is the border between fine and coarse grained soils. Practically, the beach becomes very heterogenous in fines contents both in the vertical and horizontal direction and it is seldom that the theoretical particle size segregation occurs. This is an effect from the depositional process, which are hard to control and is influenced by many factors (Vick, 1990).
Connected to the discharge procedure is also the fact that different in-place densities will be created in the beach, depending on how the particles settles. The factors that controls the in-place densities are the particle density, the particle size distribution and the clay content of the tailings. Because of the effects of discharge and different degrees of particle segregation, the scatter of in-place densities within one impoundment is often wide. The in-place density also increases with depth, since the tailings at great depth is compressed by later deposited layers (Vick, 1990).
Figure 1. Example of an upstream constructed tailings dam.
Stability of tailings dams
Through the years tailings dam failures have occurred at many places all over the world and in many cases with catastrophic consequences, see e.g. Blight (2010). Safety of tailings dams is therefore a major concern for all mining companies, and if stability problems occur the impact on the environment and society can be severe. The need of stable dams to hold the tailings in place can therefore not be neglected.
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locations of the phreatic surface, and some factors cannot easily be changed afterwards if the desired low phreatic surface is not obtained. As discussed above, the particle size segregation will determine the particle size distribution at various distances from the discharge and at various depths. With a high particle size segregation in the beach, fine particles settle far from the dis-charge and coarse particles settles close to the disdis-charge, i.e. that the fines content are lower closer to the discharge. This leads to that the hydraulic conductivity will be higher closer to embankment and a lower and less dangerous phreatic surface can be obtained in the beach and in the embankment. So, to control the phreatic surface in the embankment, which is critical to obtain stable tailings dams, the particle size distributions in the beach are a key issue for all de-posited layers of tailings. Furthermore, the permeability is also affected by the in-place density. Vick (1990) discusses that both coarse and fine grained tailings shows a decrease in permeability as the void ratio decreases, i.e. as the dry density increases. For fine grained tailings this decrease is often larger, since fine grained tailings are more compressible.
4 Behaviour of tailings
Even though tailings are a crushed and grinded material it can still be described and tested by the same theories as natural geological materials. The biggest difference is the angular shape of the particles, which comes from the crushing and grinding processes during extraction.
The material behaviour of tailings has been studied before, but not with fines content or density effects as main focus. Rodriquez (2016) studied the influence of the particle shape on the me-chanical behaviour as the main focus and discussed that when roundness of particles increases the soil strength decreases. Hence, the more angular shape of particles, the more interlocking forces and higher strength. It was also discovered that the angular shapes of the tailings lead to a degra-dation in form of breakage under shearing and compression. Besides the reduction of the particle size in the tailings during breakage it was shown that particle shape changes occur only for small particles sizes (0,063 mm). Furthermore, Rodriquez (2016) presented that the effect of the par-ticle sizes on the friction angle was hard to determine with empirical relations, since the results were conflicting. With empirical relations, an increase in particle size lead to an increase in fric-tion angle if the morphology (larger scale of shape) of the particles is used while it at the same time leads to a decrease in friction angle if the roundness (smaller scale of shape) of the particles is used.
The work of Bhanbhro (2017) included some studies of uniformly graded copper tailings in the sand fractions, where mechanical behaviour for respectively particle size were tested. Just like Rodriquez (2016), particle breakage occurred in compression and in shear, the breakage became larger for larger particle sizes. It was also discovered that the friction angle did not change for different particle sizes, when the uniformed specimens were tested in simple shear and in triaxial tests. Bhanbhro (2017) suggested that a future study could investigate the impact of the particle size on the material behaviour through constructing specimens with different percentage of each particle size.
Motivation of the study
As discussed above, the fines content and the in-place densities affect the material behaviour in strength, compressibility and permeability. Therefore, it also exists a connection between the material behaviour and deposition of tailings, since the deposition and discharge control the fines content and the in-place densities. A study of the effect of fines content and density on the material behaviour of tailings can therefore show how the discharge and deposit affects the ma-terial behaviour of the tailings in the beach.
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material, which can be used for any dam construction where the tailings are used as a construc-tion material.
1.2
Aim and objective
The aim of this master thesis is to study how the material behaviour of tailings are affected by different fines contents, FC, and different densities, ρ. Specifically, how does fines content and density affect
• strength behaviour of tailings? • compressibility of tailings? • permeability of tailings?
In order to study this, there is a need to conduct laboratory tests on specimens with different fines contents and densities. Results from the tests can then be analysed and compared, to see how the fines content and density affects the material behaviour of tailings. Objectives for mak-ing this possible are to
• Conduct a case study, with purpose to sample and make a geotechnical classification of the sampled tailings
• Select materials to study – fabricate specimens with different span of FC and densities • Study the strength characteristics in triaxial and simple shear tests under drained
condi-tions
• Study the compressibility characteristics in oedometer tests
• Determine the hydraulic conductivity in constant head tests, to study the permeability characteristics
1.3
Delimitations
The laboratory studies in this thesis have been conducted on iron ore tailings, from a specific impoundment. The exact result of the material behaviour for tailings with different fines contents can therefore not be directly used for other tailings, although the behaviour itself perhaps is similar in a larger scale. Different tailings have different characteristics in e.g. particle shapes, particle strength, plasticity etc. (Vick, 1990), which makes it possible to have variations in mate-rial behaviour between different types of tailings. The mindset in which the tailings are studied in this thesis can though be used to study the behaviour of other types of tailings.
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2
SELECTION OF MATERIALS
2.1
Case study – Kiruna Tailings
The tailings that have been studied in this thesis have its origin from the tailings impoundment in Kiruna, which is owned and drifted by LKAB. Mining is done underground and has its focus on iron, from an ore type that mainly consists of magnetite. After the ore has been transported up to the surface it is first crushed and sorted into particles smaller than 10 centimetres. After this initial sorting, particles that only consist of waste rock are drily separated from ore. The remain-ing ore is crushed and screened into even smaller particles and is thereafter ready for the con-centration plant. In the concon-centration plant the ore is grinded in several stages in order to obtain really fine particles and at the same time everything is mixed with water, which makes it possible to separate impurities from the concentration of ore. After some final stages of flotation for further separation, the concentrated ore proceeds to the pelletizing plant (LKAB, n.d). The left-overs, i.e. the tailings mixed with water, from the concentration plant are then pumped as a slurry towards a dewatering stage, where a thickener removes excess water. When the slurry has the correct water content, the tailings are further pumped and discharged at the impoundment. The tailings impoundment in Kiruna, see Figure 2,
are partly surrounded by tailings dams and partly by natural topography. Discharge of tailings are con-ducted by spigotting, mainly from the tailings dam in the northern part of the impoundment. There-fore, the need of raising the dams are also concen-trated to the northern dams. The dams are currently raised with the upstream construction method, using previously discharged tailings if possible. In the east-ern part of the tailings impoundment, excess water from the plants are discharged through a gutter. Af-ter the discharge of tailings in the northern parts of the impoundment, the tailings particles settle as the water continues in the south direction. Furthest south, all particles have more or less settled and the water is led through spillways down to a clarification pond.
2.2
Sampling and geotechnical classification
SamplingSampling was conducted during December 2017, together with a site visit around the tailings impoundment and its surrounding dams. In two points, point A and B in the same section, samples of unfrozen tailings were taken. Point A is located 20 meters from the dam crest and hence 20 meters from the discharge. Corresponding distance for point B is 60 meters. Further information about the sampling points are presented in Table 1.
7
Table 1. Information about the sampling points.
Information Sampling point
A B
Section 21+000 21+000
Distance from discharge 20 m 60 m
Northing* 7528630,13 7528595,08
Easting* 144873,36 144855,42
Elevation* 536,33 535,45
Date of sampling 2017-12-12 2017-12-11
Frost depth 0,35 m 0,15 m
Sample taken from depth to
depth 0,40 – 0,60 m 0,20 – 0,40
Dimensions of sample pit
(Length x width x depth) 0,4 x 0,35 x 0,2 m 0,4 x 0,3 x 0,2 m
Number of sampling tubes 3 3
Number of sampling buckets 1 (around 20 kg) 1 (around 20 kg)
Number of sampling bags 2 (around 2 kg) 2 (around 2 kg)
Other observations Coarser particles at first sight, a layering with finer tailings was observed in the bottom. Relative “dry” tailings and more firm. Tubes needed to be tapped down.
Relative “wet” tailings. Finer particles and homogenous tailings in the sampling pit. Relative “loose” tailings, tubes were pressed down by hand.
* Coordinate system: SWEREF 99 20 15 in plane, Height system: RH2000
8
Figure 3. Sampling procedure to remove frozen tailings. To the left (a) drilling in a rectangle pattern and to the right removal of the frozen block.
First, with the use of sample tubes for undisturbed sampling, samples were collected to obtain a rough indication of the bulk density and dry density in the field. This was done in each point, by pressing down three tubes into the undisturbed tailings and then carefully release them from the remaining tailings, see Figure 4. If the tube, with diameter 5 cm and height 17 cm, was not fully filled the deviation from the full height was noted, in order to later calculate the correct volume of soil. The tubes were then sealed with appurtenant caps and tape, in order to not lose any water or material, before weighing was conducted in the laboratory.
9
When the tubes had been collected, more disturbed samples were taken from each point. Around 20 kilograms of disturbed tailings were sampled in each point, mostly gathered in large buckets. For water content determination, around 2 kilograms were collected in double sets of plastic bags to eliminate diffusion of water from the samples.
Density in field
Both dry density and bulk density were determined from the sealed tubes collected during sam-pling. The results are presented in Table 2. Based on the sampling method for these tubes, see Figure 4, the determination of these densities should not be seen as an exact value, more like an indication of densities in field. Bulk density, ρ, was determined with equation (1)
ߩ =ܸ݉
௧௨
(1) Similarly, the dry density, ρd, was determined with equation (2)
ߩௗ = ܸ݉௦ ௧௨
(2) where m is the total mass of the sampled tailings, mS is the mass of dry tailings and Vtube is the
volume of the tube. Particle density
The particle density for the tailings was determined with the fluid pycnometer method. From each sample point three tests were conducted and then the average value of the particle density in each point was calculated. The fluid used was distilled water, that were de-aired during boiling before being used.
The particle density, ρS, was then calculated with the principle presented in equation (3) and
the result is presented in Table 2.
ߩ௦ = ܸ݉௦ ௦
(3) Water content
Water content was primarily determined from the samples that were collected and placed in double sets of plastic bags. Besides those samples, water content was also determined from the sampling tubes. Water content, w, is determined by equation (4)
ݓ =݉݉௪
௦
(4) where mW is the mass of water in the sample. Results are presented in Table 2.
Porosity, void ratio and degree of saturation
10 Porosity was calculated with (5)
݊ =ܸܸ = 1 − ߩߩௗ
௦
(5) Void ratio was determined with (6)
݁ =ܸܸ
௦ =
ߩ௦
ߩௗ− 1
(6) Finally, degree of water saturation for each tube was determined with (7)
ܵ= ܸܸ௪ =
݉௪ ߩ௪ ∗ ݊ ∗ ܸ௧௨
(7) In Table 2, the calculated values of porosity, void ratio and degree of water saturation is pre-sented.
Table 2. Results of densities, water content, porosity, void ratio and degree of water saturation.
Particle size distribution and fines content
The particle size distribution for the tailings were separately determined for the samples from point A respectively point B and the result is presented as the yellow respectively the red curve in Figure 5. Wet sieving was combined with dry sieving, to properly separate fine and coarse particles. Particle sizes smaller than 0,063 mm were determined through sedimentation analysis with the pipette method, using tetra sodium diphosphate as dispersing agent.
Besides the particle size distribution curves that were determined for the samples within this thesis, LKAB also conducted their own sampling of frozen tailings with purpose to determine the particle size distribution in different sections and at various distances from the discharge. Of their samples 10 were taken in the same section as point A and B, from about 0 to 100 meters from the discharge point and those particle size distribution curves are presented as the dimmed and dashed curves (Prov 1 – 10) in Figure 5.
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Figure 5. Particle size distribution in the sampled section. A and B are samples within this thesis, remaining samples (Prov 1-10) are from LKABs own particle size distribution.
The fines content, percentage of particles smaller than 0,063 mm, varies relative much for the analysed samples. As can be seen in Figure 5, there exist a span of FC between 35 – 93 % for the samples taken at the section. The fines content as function of distance from discharge is presented in Figure 6. It can be seen that it does not exist any clear and consistent trend in fines content as function of distance from discharge.
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2.3
Material selection
It was decided that three materials with different fines content should be studied in strength, compression and permeability. These materials were determined in a way that made it possible to create a large span of fines content to study.
2.3.1
Span of fines content (FC)
The results of particle size distributions presented in Figure 5 and fines content with distance from the discharge in Figure 6 indicates that the fines content clearly varies in the beach. Based on this, it can be said that it is possible that tailings have fines content up to 90 % in the beach and hence this was determined to work as an upper limit for the span of fines content.
With the upper limit determined, the lower limit was chosen to a fines content of 10 %. This was done to create a large span of fines content to study, even though fines content of this magnitudes were not discovered in field. It is however possible to obtain low fines contents like this by using cyclones to separate fine particles from coarser particles. Vick (1990), discusses that FC as low as 3 % can be obtained by a two – staged cycloning.
With a span of FC between 10 – 90 %, the three materials selected for further studies became • Material 1 – FC 90 %, original material from sample point B
• Material 2 – FC 50 %, fabricated material • Material 3 – FC 10 %, fabricated material
In Figure 7, the particle size distributions for the three materials are presented. The fabrication of material 2 was conducted with the fines, i.e. particles smaller than 0,063 mm, from sample B as basis. Corresponding was done for material 3, but with the fines from sample A. Particle sizes of the fines was determined with the pipette method. Thereafter these particle sizes were recal-culated as a weight percentage of the total weight of respectively material and the weight of coarser particles were added in exact amounts to fit the particle curves presented in Figure 7.
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2.3.2
Span of densities
It was determined in the early stages of planning that laboratory tests performed for strength evaluation, i.e. triaxial and simple shear tests, were going to be tested for one density. The reason for that is that the critical state friction angle, later described in subsection 3.1, is independent of density. Laboratory tests for compressibility and permeability evaluation were however deter-mined to be tested for a span of densities.
Initially the goal was to achieve the same span of dry densities for all the three materials. After some compaction tests, it was however discovered that it was incredible difficult to reach the same dry densities for all three materials. The outcome of this was that the span of dry densities became material specific. To get an idea of possible minimum and maximum dry densities for respectively material some density tests were conducted in the laboratory.
The minimum dry density was determined by pouring dry material into a mold with known volume and then calculate densities with the weight of the poured material, in agreement with the standard ASTM D4254-00. An exception from
the standard was however that a smaller mold, with height of 10 cm and diameter of 5 cm (see Figure 8), was used. The test was repeated until the obtained minimum dry density were more or less constant. In Table 3, the obtained minimum dry densities for re-spective material from the test is presented.
The maximum dry densities were first attempted to be determined with pouring dry material and the use of a vibrator table, according to the procedure of standard ASTM D4253-00. However, this resulted in maximum densities which became unreasonably low. New attempts of finding maximum densities were conducted with a more high-energy compaction technique, using a hand-proctor and dry tamping each layer which was poured into the mold. With this technique the reached maximum dry density became according to Table 3.
Table 3. Minimum and maximum dry density and corresponding void ratios for respective material.
In table 3, the corresponding void ratios have also been calculated. Minimum and maximum void ratios can be used for further determination of relative densities for the material tested in
Material Minimum dry density [t/m3] Maximum void ratio, e max
Maximum dry
density[t/m3] Minimum void ratio, e min
1 1,15 1,60 1,84 0,62
2 1,32 1,27 2,03 0,47
3 1,45 1,05 2,01 0,49
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the laboratory tests. The relative density, ID, is calculated with equation (8) (Bolton 1986, Vick
1990).
ܫ = ݁݁௫ − ݁
௫ − ݁∗ 100 [%]
(8) where e is the void ratio in the current situation, e.g. for the lab specimen or in field. The index max corresponds for the loosest state of the material and the min for the densest state of the material. With this definition a relative density of ID = 100 % means that e.g. the specimen has
the densest configuration possible for that material and contrary ID = 0% means that the loosest
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3
LABORATORY STUDY
3.1
Mechanical behaviour
Mechanical behaviour of the tailings, studied in this thesis, can further be divided into charac-teristics in strength and characcharac-teristics in compressibility. Strength characcharac-teristics have been de-termined through triaxial tests and simple shear tests, both under drained conditions. Compress-ibility characteristics have been determined through oedometer tests.
Strength and critical state theory
The strength for any material is commonly defined as the maximal shear stress, τ, that the material can sustain. For soils and other frictional materials, the drained strength is however increasing with increasing normal effective stress, σ’, and hence the ratio between τ and σ’ is more important to study (Atkinson, 1993). The strength of tailings, i.e. the maximal shear stress that it can sustain, can be described with the Mohr-Coulomb criteria, see equation (9), and hence τ will in most cases become a function of σ’ and the friction angle, φ’. The cohesion intercept, c’, is zero for majority of soils, and if true cohesion is present it is only a few kPa (Atkinson, 1993).
߬ = ܿᇱ+ ߪᇱ∗ ݐܽ݊߮ (9)
When a soil specimen is sheared in e.g. triaxial test it will eventually reach a state where it continues to deform with constant volume and at constant shear stress (Atkinson, 1993). This state is called the critical state, or in some literature the steady state. Idealized shearing behaviour for a dense and a loose specimen is presented in Figure 9. Theoretically, regardless of the initial state, loose or dense, specimens of the same material will reach the same critical state after a certain amount of straining, see point A in Figure 9. In general, dense materials that are sheared shows a significant peak in shear stress, followed by a strength reduction to the critical state. Loose materials are not showing any peak, instead they will reach the maximum shear stress and then continue to distort at constant shear stress (Atkinson, 1993).
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Figure 9. Idealized shearing and straining behaviour under drained conditions for a dense specimen (yellow) and a loose specimen (orange).
For drained shear tests, the volume change can also be connected to the critical state theory. It has been noticed that the shear stress, point D in Figure 9, occurring at the minimum point of volume change for a dense specimen, are of the same magnitude as the stress at critical state (Atkinson, 1993). Therefore, one way to interpret the critical state is to study the stress situation at the minimum point of volume change. Another way, is to look at large strains and see where the volume change and the shear stress becomes constant, point A in Figure 9, since this would theoretically be considered as the critical state.
As discussed above, the critical state reached is independent of the initial conditions, i.e. com-pacted density of the specimen tested. The peak values in strength, showed for specimens with dilative behaviour, will however not have the same independency of the initial conditions. Sim-ilar to the critical state, it exists a relation between the peak value in strength and the volume change. This relation is that the peak value in strength interrelates with the point of the maximal dilation angle, ψmax. The dilation angle, ψ, will at any point during shearing be defined by
equa-tion (10), i.e. as the gradient to the εvol and εaxial curve presented in Figure 9. Since the minus
sign is added in equation (10) a positive dilation angle will be associated with dilation, i.e. neg-ative volume straining (Atkinson, 1993). Bolton (1986) presented that the peak friction angle, at peak failure for dense sands can be seen as an extra angle of shearing which is correlated to the rate of dilation of the soil. The rate of dilationis a function of the relative density, ID, the mean
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as an extra angle of shearing it will also be affected by the mineralogy. Bolton (1986) discuss that the critical state friction angle is roughly 33° for quartz and 40° for feldspar.
߰ = −݀ߝ݀ߝ௩
௫
(10) Mohr circles of stress, see Figure 10, is fundamental when it comes to analysing the stress con-dition on a loaded soil specimen in a triaxial cell. During a triaxial test, the largest, σ1, and the
smallest, σ3, effective principal stress at an arbitrary axial strain is all that is needed to plot
corre-sponding Mohr circle. This arbitrary axial strain, no matter if it is at small strains, at peak failure or at critical state can be used to calculate the friction angle for the current stress condition and by this it is also possible to calculate the friction angle at any axial strain. In these cases the term mobilized friction angle, φ’mob, is often used, considering that the specific friction angle is
mobi-lized during shearing at the current axial strain. The mobimobi-lized friction angle at any axial strain with corresponding stress condition, σ’1 and σ’3, can be calculated (Atkinson, 1993) with
equa-tion (11)
߮ᇱ = ݏ݅݊ିଵ൬ݐ
ݏ൰ (11)
where ݐ = ଵଶሺߪଵᇱ− ߪଷᇱሻ and ݏ = ଵଶሺߪଵᇱ+ ߪଷᇱሻ are defined from Figure 10 as the maximum shear
stress respectively the effective mean stress at the current stress condition. Strength parameter evaluation of φ’mob according to equation (11) are also referred to as the secant strength or secant
φ’ in some literature. Secant comes from the fact that it is the gradient of one stress point and the origin, and differs from the traditional tangent strength values, φ’ and c’ which are valid for a specific stress interval. If a test series, with specimens sheared for different consolidation stresses are used, it is also possible to evaluate the friction angle from inclination of the best fit linear regression line to the Mohr circles from all the tests in the series.
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Research on strength behaviour for natural sand-silt mixtures have in some cases focused on a transitional fine content, TFC. It is based on an intergrain concept proposed by Thevanayagam (1998), which assumes that all particles in a sand with fines are not actively participating in the force chain which transfer load in the soil skeleton. Therefore, all particles will not contribute to the shearing resistance. At fines contents below TFC the voids are filled with fine particles which are assumed to not participate in the shearing resistance. Hence the soil will theoretical act as a sand. For fines contents above TFC the sand particles are assumed to be in the voids and does not contributing to the strength, which leads to a silty behaviour. Yang, Lacasse and Sandven (2006) discovered that their sand silt mixtures had a TFC about 30%, based on com-parisons of fines contents and steady state lines. Furthermore, Yang et. al (2006) also calculated TFC with index data, in form of void ratios and specific gravity. The result of this became TFCs between 19 – 36 % for the same sand-silt mixture, based on extreme values of the host sand and host silt.
Polito and Martin (2001), studied the effects of fines content on cyclic resistance and found out that it existed a limiting silt (i.e. fines) content of about 35 %, similar to the TFC, which was a border between two different patterns in behaviour. It was found out that for fines content larger than the limiting fines content the cyclic resistance was significant lower than for specimens below the limiting fines content. Finally, Polito (1999) analysed the TFC based on index data from 37 sands and 5 silts, which lead to a combination of 185 sand-silt mixtures. The results of this indicated that the TFC varied between 25% - 45 % for the different sand – silt mixtures. Yang et. al (2006) did however conclude that TFC only calculated with index data are insuffi-cient, since there exist uncertainties in determination of void ratios.
Compression and consolidation
Compression in soil can be described by the consolidation process, where the successive trans-ferring of load from pore water to soil skeleton in a loaded saturated soil body is described. This can also be considered as the volume change due to change in effective stress in a saturated soil body. When a soil body is loaded quickly with an increase in total stress, ∆σ, and immediate drainage is not possible it will give rise to an excess pore pressure, ∆u. The effective stress, ߪᇱ=
ߪ − ݑ will immediately not be affected since ∆σ = ∆u, and therefore the volume of the soil remains constant. With time the excess pore pressure will start to dissipate and then the effective stress will increase in the same rate. As the effective stress increases, the volume will start to decrease. When ∆u = 0 the σ’ have increased the same magnitude as the ∆σ and the volume change have decreased to its minimum and become constant (Atkinson, 1993).
Results from one – dimensional oedometer tests, where consolidation is studied, can be plotted as the normal consolidation curve represented by the compression at a certain effective normal stress (Axelsson et. al, 2016). The compression will be the same as the axial straining, εa, since
the compression in oedometer tests are totally restricted in the lateral direction. At an arbitrary point on the normal consolidation curve the relation between compression and effective stress can incrementally be described with equation (12) retrieved from (Axelsson et. al, 2016).
݀ߪᇱ = ܯௗ∗ ݀ߝ (12)
where Moed is known as the oedometer modulus or the tangent modulus, since it is the modulus
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clays, the entire σ’- εa curve can be described by the relation in equation (13), where σ’ref is by
tradition taken at 100 kPa and hence Moedref is the oedometer modulus at 100 kPa. β is called the
stress exponent and varies between 0,5 for sands and 0 for clays (Axelsson et. al, 2016). ܯௗ = ܯௗቆ ߪ ᇱ ߪᇱ ቇ ଵିఉ (13)
3.2
Triaxial test
Triaxial apparatusThe essence of triaxial tests are that the principal stresses are known during the test. In ordinary triaxial tests the soil specimens are cylindrical with a height – diameter ratio of 2, and a principal stress situation presented in Figure 11. This principal stress situation holds for active compression tests where the axial stress is larger than the radial stress on the specimen. The smallest principal stress, σr = σ3, is applied through the cell pressure and since the specimens are cylindrical the
intermediate and the smallest principal stress will always be of the same magnitude. Furthermore, the cell pressure acts on all planes on the specimen and therefore the largest principal stress, σ1,
is applied by adding an external stress, σd, in the axial direction. Therefore, the largest principal
stress becomes: σa =σ1 = σd +σ3 (Lade, 2016). It is also important to see that, σd = σ1 - σ3, which
is known as the deviator stress.
A soil specimen tested in triaxial tests must always be as fully saturated as possible and sealed with a membrane from the cell pressure. The membrane is essential to create the correct stress con-ditions and makes it possible to have control over the volume changes for drained tests. To get a satisfying saturation of the specimen a back pressure can be applied, once the specimen has been installed in the cell. The back pressure will make it possible to raise the pore pressure under controlled forms and force air in the pores to solve in pore water. Back pressure is applied through porous discs at one end of the specimen. During shearing the back pressure connection remains open for drained tests, making it possible to study the volume change of the specimen. The saturation of a specimen can be checked by investigate the pore pressure coefficient or B – value, which is 1 for fully saturated specimens and <1 for partially saturated specimens. The B – value is defined with equation (14) by assuming that the reduction of the soil skeleton when ∆σ is applied is equal to the reduction of pore volume and the fundamental assumptions that soil particles are incompressible and that no drainage occurs (Craig, 2004).
ܤ =∆ݑ∆ߪ (14)
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some amount of straining exceeds the shear strength and the strength of the soil can be evaluated (Lade, 2016).
Figure 11. Dimensions and principal stress situation on a specimen for an active compression test
Triaxial tests in this thesis were conducted with a hydraulic triaxial apparatus for controlled stress paths developed by Bishop and Wesley. This apparatus applies axial stress, σa, through increasing
the pressure in a lower chamber, which is sealed from the cell and the piston chamber with bellofram seals. When the pressure in the lower chamber is increased, the piston presses the pedestal upwards and hence an axial stress is applied to the soil specimen (Donaghe, Chaney and Silver, 1988).
Conducted triaxial tests
Triaxial tests were conducted as isotropic consolidated-drained compression tests, all at disturbed and remoulded specimens. For material 1-3 respectively, a set of 3 tests for one dry density was conducted at the consolidation stresses 50, 100 and 150 kPa. Preparation of specimens and setup of tests have been conducted in the same manor for all specimens.
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Table 4. Prepared dry densities and obtained B - values for all triaxial tests
When compaction was completed a pre-saturation phase began, where constant head water pressure was used. For material 1, the water was inserted from the top. Since that resulted in low B-values, a new technique with inserting water from the bottom was tested for material 2 and 3. When a specimen was considered to be fully saturated, the top cap was placed above the porous discs and o – rings sealed the membrane against the cap. In Figure 13, a com-pletely prepared specimen is presented.
Each test began with a pre-consolidation phase (cell pressure 20 kPa, back pressure 10 kPa), to partly see that no leakage occurred and partly to stabilize the specimen. Then a satu-ration ramp (targets: cell pressure 215 kPa, back pressure 200 kPa) was conducted with a time step of 120 minutes to reach the target pressures. This was followed by a B – check, in order to check the degree of saturation of the specimens according to the definition in equation (14). Obtained B – values for material 1 was 0,59 – 0,82, corresponding for ma-terial 2 was 0,92-0,98 and 0,69-0,78 for mama-terial 3. The
specimens from material 1 and 3 have in other words not been successfully saturated, since in practice B – values above 0,9 is considered as really good.
Test Material 1 Material 2 Material 3
ρd [t/m3 ] [-] e I D [%] ρ d [t/m3 ] [-] e I D [%] ρ d [t/m3 ] [-] e I D [%] 50 kPa 1,67 0,79 83 1,77 0,69 72 1,91 0,57 86 100 kPa 1,63 0,82 78 1,80 0,66 76 1,89 0,58 83 150 kPa 1,64 0,82 80 1,80 0,66 77 1,89 0,58 84
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Thereafter, the consolidation began (back pressure: current pressure after B-check, cell pressure: back pressure + consolidation stress) and this phase lasted until no significant changes in volume or pore pressure occurred. After docking of the
speci-men had occurred, shearing began at a constant defor-mation velocity of 0,015 mm/minute and a maximal ax-ial straining limit set to 20 %.
The output of the triaxial tests have been evaluated with the main focus on the friction angle at critical state. The critical state (CS) have been evaluated at stress condi-tions that occurs at the minimum volume (CS – min. volume) and for stress conditions at large strains where the critical state “graphically” (CS – large strains) have been reached. It was discovered that the exact value of the minimum volume strain acts for a relative large span of axial strains. Because of this the corresponding stresses were taken at the largest axial strains at the span of min-imum volume, just before the specimen starts to dilate, see Figure 14. Graphically evaluation should theoreti-cally be done at the point where the volume becomes constant. In practice, the results have in most cases not
shown a constant volume and evaluation of stresses at critical state for large strain have hence been made where a clear distinction in the dilation angle have occurred. For some test, where this distinction has not existed, the stress conditions have been taken at the largest strains. The friction angle was also evaluated at the peak strength (PS), by choosing the stress state as the absolute maximum shear stress.
Figure 14. Selection of axial strain at minimum volume strain for evaluation of critical state at minimum volume
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3.3
Simple shear test
Simple shear apparatus
The simple shear test, or direct simple shear test, was developed with the idea of avoiding non-uniform stresses and strains that occurred in direct shear box tests (Atkinson, 1993). It basically exists two types of apparatus for simple shear tests, the Swedish SGI – type and the Norwegian NGI – type (SGF, 2004). The simple shear apparatus used for the test in this thesis was of the NGI (Norwegian Geotechnical Institute) type, fabricated by Geonor. The apparatus has though been provided with some modifications, considering measurements of pore pressure during shearing. In Figure 15a and Figure 15b, a specimen tested in the NGI – type is shown.
Figure 15. a) specimen tested in simple in the NGI apparatus. b) schematic picture of specimen tested in NGI apparatus.
Regardless the type of apparatus, specimens tested normally have dimensions of 50 mm in di-ameter and 20 mm in height and are during the test located inside a membrane. Besides the membrane, the specimens are also confined by e.g. rings or wires which prevents lateral defor-mations of the specimen. Generally, the specimens tested first undergoes a consolidation phase by an applied normal stress, σn, at the top of the specimen. Thereafter the shearing phase begins
by applying a horizontal force on the upper plane of the specimen. This horizontal force divided by the cross sectional area of the specimen, creates the shear stress, τ. As shearing progresses the shear strain, ϒS, will be defined according
to equation (15), as the angle change in radians created by the displacement, s (SGF, 2004). The height, h, of the speci-men is according to SGF (2004) fixed for undrained tests and for drained tests h is allowed to vary freely in agreement to volume changes of the specimen. In Fig-ure 16, the stresses and strains on a tested
specimen is presented. Figure 16. Stresses and strains acting on a specimen
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ߛௌ = ܽݎܿݐܽ݊ ቀݏℎቁ [ݎܽ݀] (15)
The Swedish standards for evaluating the strength from a simple shear test series conducted on the same material but with different σn, is based on the idea of plotting the stress state at failure,
i.e. shear stress τ versus normal stress σ from each conducted test. If a test has shown a distinct peak in shear stress, this τ should be chosen. However, in most drained test a truly failure seldom occurs and then τ should be chosen with a deformation criterion, which in Sweden is a shear strain at ϒS = 15 radians (SGF,2004).
Recent studies by Knutsson (2018) presented that the evaluation of strength at ϒS = 15 radians
is inappropriate. The shear stress at ϒS = 15 radians are different for specimens with different
densities, although they consist of the same material. Evaluation of friction angles therefore led to an increased friction angle with increased density, which is not supported by the critical state theory. Instead the axial strain, εa, versus the shear strain, ϒS, should be studied to find ϒS for
which corresponds to the critical state approach. In simple shear tests these points will therefore be either minimum points in volume strains for material that shows dilative behaviour or other-wise at large shear strains where it is assumed that the volume should reach its critical state. Conducted simple shear tests
The simple shear tests in this thesis were, just like the triaxial testing series, conducted on 3 specimens for each of the materials. The 3 specimens from one material were consolidated to 50, 100 respectively 150 kPa and approximately prepared to the same initial dry density. Prepa-ration of the specimens was conducted directly in the membrane on top of the bottom porous disc. Both porous discs used were provided with spikes to improve the adhesion between the specimen and the discs. Compaction was done with the same technique as for the triaxial tests by dry tamping the material in tiny layers. The prepared dry densities, when mounted in the apparatus, for each simple shear test are presented in Table 5. Further densification occurred during consolidation and hence the dry density before shearing was a little bit higher than the prepared.
Table 5. Dry densities after preparation for all specimens tested in simple shear.
When the specimens have been mounted in the apparatus they were first saturated with water, followed by a consolidation to the desired consolidation stress. Shearing were started when no
Specimen
Material 1 Material 2 Material 3
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change in height occurred, and the used deformation velocity where 0,0054 mm/minute. Shear-ing was interrupted after 5 mm of displacement.
Evaluation of the simple shear test results have been done with the critical state approach, i.e. at stress conditions at minimum axial straining, when it has been possible. In the cases where no minimum point in volume have occurred, the friction angle has instead been evaluated for large strains where a global minimum point of axial strain was present. The chosen shear stresses have then been plotted in the τ-σ’ plane together with the other specimens for the same material.
3.4
Oedometer test
Oedometer test
An oedometer tests is also called one-dimensional compression test, since the specimen is con-tained inside a stiff ring which prevents lateral displacements when load is applied. In the bottom and on the top of the specimen porous discs are installed and hence the drainage is purely vertical and one-dimensional (Atkinson, 1993).
During a oedometer test the fully saturated specimen is during the whole test lowered in a water bath, see schematically picture presented in Figure 17. The upper porous disc can move inside the oedometer ring as the applied normal stress σn creates the compression or straining, εn, in the
same direction. The current normal stress, σn, is applied through a load cap on top of the upper
porous disc and then spread to the specimen. Both porous discs are directly in contact with the surrounding water, which means that the pore water in the soil can move freely in and out of the specimen. The initial load depends on the soil tested, thereafter each load step applied should double the previous stress on the specimen. Normally, each load step is maintained for a 24-hour period or in some cases a 48-24-hour period. At the end of each load step the applied vertical stress will be the same as the normal effective stress on the specimen, since all excess pore pressure have dissipated (Craig, 2004).
Figure 17. Specimen tested in the oedometer test.
Conducted oedometer tests
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the loosest samples of material 3 have a relative density of – 66 % and is therefore in a looser state than what is possible. This is probably a consequence from the water used during compac-tion. Compaction was done using a tiny tamper and compaction in layers. When the specimens had been prepared and filter stones had been placed above and beneath the material they were placed in a water bath to get fully saturated. After a 24-hour period, the loading process began.
Table 6. Dry densities for specimens tested in oedometer test.
Specimen
Material 1 Material 2 Material 3
ρd [t/m3] I D [%] [t/mρd 3] I D [%] [t/mρd 3] I D [%] 1 1,36 41 1,46 28 1,23 - 66 2 1,49 61 1,75 70 1,48 5 3 1,67 83 1,79 76 1,64 41 4 1,78 94 1,98 95 1,87 80 5 - - 1,91 86
Incremental loading steps between 10 – 640 kPa were used, where the load increased to twice its size between each step. The load step of 20 kPa were acting on the samples for 72 hours, while remaining loads only acted on the sample for the traditional 24-hour period. During the test the vertical compression of the specimen was measured with strain gauges.
3.5
Hydraulic behaviour
Hydraulic conductivity and constant head test
Hydraulic behaviour, i.e. permeability characteristics, of the three materials have in this thesis been studied in form of the hydraulic conductivity, determined through constant head tests. The hydraulic conductivity, k, can be described as the seepage velocity for water passing through a soil volume (Atkinson, 1993). The value of k is derived from Darcy’s law, see equation (16), where v is the velocity of the water flowing through a soil body with the height (or length) h and the cross section area A. In equation (16), the term i is the hydraulic gradient which is the ratio between the water pressure head, H, and h (Blight, 2010).
ݒ = ݇ ∗ ݅ [݉/ݏ] (16)
The idea of the constant head test is to expose a fully saturated soil specimen for a constant water head and then measure the water flow through the specimen during steady state flow (Blight, 2010). With use of the measured flow, q, and the known values of H, h and A, equation (16) can be rewritten according with equation (17).
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Permeability tests, such as constant head tests, are possible to do with either rigid walled or flexible walled permeameters. Rigid walled permeameters are cylinders of plastic or metal, which contains the soil that is going to be tested. Flexible walled permeameters were developed to minimize risk of higher seepage against the walls (Blight, 2010), and in this case the specimen is tested in a flexible membrane inside a type of triaxial cell.
The hydraulic conductivity of a material depends mainly on the average sizes of the pores and hence mainly on the particle sizes of the material. Large particles will in general have large aver-age size of pores and the hydraulic conductivity will then be high. Contrary, finer particles lead to smaller average size of the pores and the hydraulic conductivity will be lower. Besides particles sizes, the particle shapes and soil structure will also affect the hydraulic conductivity (Craig, 2004). Blight (2010) further discusses about how the hydraulic conductivity of a soil is affected by factors that are hard to recreate in a small scale laboratory tests. These factors are for instance layering effects, shrinkage cracks, fissures etc., which all can occur for deposited tailings as well. In the literature there exist empirical relations for computation of k. Hazens formula, see equa-tion (18), computes the hydraulic conductivity based on the particle size distribuequa-tion of the material. More specific it uses the smallest particles in the material for determination of k.
݇ = ݀ଵଶ ݉/ݏ (18)
where d10 is the particle size in mm for which 10 % of the material is finer than. However, in a
study on the behaviour of Swedish tailings by Bjelkevik & Knutsson (2005), it was concluded that k cannot be determined well with empirical relations such as Hazens.
For natural soils, the effects of fines content on k have been well studied. Belkhatir et. al (2014) discovered that k decreases linearly with increasing fines content for soils at the same relative density and that FC=50 % can have k - values four times smaller than FC=0%.
Conducted Constant Head tests
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Table 7. Dry densities for specimens tested in constant head test.
Specimen
Material 1 Material 2 Material 3
ρd [t/m3] I D [%] [t/mρd 3] I D [%] [t/mρd 3] I D [%] 1 1,22 16 1,44 25 1,42 -11 2 1,38 45 1,71 65 1,60 32 3 1,70 86 1,86 83 1,71 54 4 1,84 99 1,98 95 1,96 94
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4
RESULTS
4.1
Mechanical behaviour
4.1.1
Triaxial tests
Results from the drained triaxial tests in this study are presented in Figure 18, as the stress ratio (σ´1/ σ´3 ) respectively the volumetric straining (εvol) plotted against the axial strain (εa) during
shearing. It can be seen that material 3 can sustain considerably higher shear stresses than material 1 and material 2, which sustains relative similar stress magnitudes. All three materials shows a peak value in strength, although the reduction in shear strength is more distinct for material 3 and less distinct for material 1. This have partly to do with the initial density, but since the relative density is in the range of ID=72-86% for all three materials it still shows an indication
that material 3 shows a more dilative behaviour than the other two materials. Studying the vol-umetric straining, it can be seen that the minimum point of volume change occurs at small axial strains (≈<2%) for material 3, while corresponding axial strains for material 1 and 2 are a bit larger (≈<6%). The red curve for material 1 is a specimen tested for a consolidation stress of 100 kPa, but since leakage occurred under shearing a new specimen was tested for 100 kPa.
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In Figure 18, the chosen stress states for critical state at minimum volume (CS – min. volume) respectively critical state at large strains (CS – large strains) are marked with a rhomb respectively a circle. The chosen stress states at peak strength (PS) are marked with a triangle. In Figure 19, Figure 20 respectively Figure 21 these stress states have been plotted as Mohr circles. For the two types of critical state stresses, best fit – linear regression lines have been created from the stress points from different consolidation stresses. The inclination of these lines will then also be the critical state friction angle but can be seen as an average based on three tests.
Figure 19. Mohr circles of stress for the critical state (CS) and peak (PS) stress conditions obtained for material 1.
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Figure 21. Mohr circles of stress for the critical state (CS) and peak (PS) stress conditions obtained for material 3.
The Mohr circles in Figure 19 - Figure 21, once again shows the difference in sustained stresses between the materials. By comparing the stress states between material 1 and material 2 it can be seen that the differences in stresses are small, especially at critical state and confining stresses of 50 and 100 kPa. However, the trend is that material 1 shows less strength than material 2. Since material 3 shows highest strength, the overall trend is that the strength increases with decreasing fines content FC.
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Table 8. Evaluated friction angles both from the best fit lines and from a stress state from a single test.
Evaluated from
Friction angle, ϕ, [°]
Material 1 Material 2 Material 3 CS - min. volume Best fit 34,0 35,1 37,3 CS – Large strains Best fit 34,1 34,9 39,1 CS – min. volume Secant, 50 kPa 33,3 32,7 35,9 CS – Large strains Secant, 50 kPa 33,6 34,1 40,3 PS Secant, 50 kPa 36,9 36,3 48,9 CS – min. volume Secant, 100 kPa 33,4(33,3*) 34,1 36,7 CS – Large strains Secant, 100 kPa 34,7(30,1*) 34,6 39,3 PS Secant, 100 kPa 36,1(35,4*) 36,4 47,2 CS – min. volume Secant, 150 kPa 34,3 35,7 37,7 CS – Large strains Secant, 150 kPa 34,0 35,1 38,9 PS Secant, 150 kPa 36,6 37,7 45,8
*values from test that leaked during shearing (not presented in Figure 22)
Evaluated friction angles verifies the previous statement of fines content and strength. As can be seen in both Figure 22 and in Table 8, material 3 have the highest friction angles at critical states, evaluated both from the best fit linear lines and the secant parameters. Material 1 have the lowest friction angles at critical state, although corresponding friction angles for material 2 only are slightly larger. For some secant friction angles exceptions exist, where material 1 shows larger angles than material 2. Peak values of the friction angle are relative similar between material 1 and 2, material 2 in general shows a little bit larger peak friction angle. Material 3 have peak friction angles which are significant larger than the two other materials. Since the relative den-sities are similar for the three materials, comparison of peak and dilatancy is not totally incorrect.
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4.1.2
Simple shear tests
Results from the drained simple shear tests are presented in Figure 23, as the shear stress versus the shear strain respectively the axial strain versus the shear strain. The axial strain, i.e. the change of height of the specimen, can be seen as the change of volume since the cross sectional area of the specimen is assumed to be constant during shearing.
Figure 23. Results from simple shear tests. Shear stress respectively axial strain versus shear strain for; a-b) Material 1, c-d) Material 2, e-f) Material 3
The tendency in Figure 23 is that material 3 sustains the highest shear stress and material 1 the lowest. The specimen of material 2 at normal stress 100 kPa is the only exception, since it shows slightly lower stress than corresponding specimen from material 1. The difference between ma-terial 3 and mama-terial 2 is not as large as from the results of the triaxial tests.
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“change in volume” corresponds relative well to the constant values of shear stress obtained at large strains.
Material 3 show a small tendency of peak values in shear stress (marked with triangles in Figure 23), although they are not distinct and does not show any clear strength reduction at larger strains. Studying the volumetric change (axial strains) versus the shear strain, it can be seen that the specimens from material 3 first contracts at small shear strains and then after a minimum point in volume shows a typical dilative behaviour with an increase in volume. According to the critical state theory, this would be a typical peak – strength reduction behaviour in shear stress. It is hard to know if the stress state at minimum point of volume change corresponds to a critical state stress, since it is hard to extrapolate at larger strains. One unexpected tendency is shown for the specimen of material 3 and consolidation stress of 150 kPa, where a volume decrease occurs once again at larger strains after the continuously height increase. No reasonable explanation for that behaviour has been found.
The chosen stress states in Figure 23, are plotted in a shear stress, τ, and effective normal stress, σ’, plane and the result is presented in Figure 24. An adaption of the best fit linear lines to each stress state have been done and is also presented in Figure 24. The inclination of the best fit – lines presented in Figure 24, are evaluated as the friction angle for respectively material. These results are presented in Table 9 together with secant friction angles evaluated from one test at the chosen stress states in Figure 23. It can directly be said that the “frictions angles” from the simple sheared tests are significant lower than friction angles from the triaxial test. Therefore the “friction angles” obtained from simple shear tests have been chosen to be called angles of shearing resistance instead.
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Table 9. Angles of shearing resistance from simple shear tests.
Evaluated from
Angles of shearing resistance, ϕ, [°] Material 1 Material 2 Material 3
Best fit - Volume 26,7 27,6 27,9
Best fit – Large strains 27,0 27,6 31,3 Secant, 50 kPa Volume 25,6 27,4 28,4 Secant, 50 kPa Large strains 25,3 29,1 33,5 Secant, 100 kPa Volume 27,0 - 25,9 Secant, 100 kPa Large strains 27,8 25,8 31,9 Secant, 150 kPa Volume - 27,7 28,8 Secant. 150 kPa Large strains 26,9 28,2 30,8
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4.1.3
Oedometer tests
The normal consolidation curves from the oedometer tests is presented in Figure 25. The trend for respectively material is that with decreasing dry density the axial compression increases. As can be seen for material 2 there exist an exception from this since ρd=1,75 t/m3 have been
compressed less than both ρd=1,98 t/m3 and ρd=1,79 t/m3. The reason for that are probably
connected to the measuring of the strain, either problems with the load cap and the top porous disc or problems with the gauge.
Furthermore, if comparing the materials between each other it can be seen that in general ma-terial 1 are compressed the most and mama-terial 3 is compressed the least. In other words, with decreasing fines content the compressibility decreases.
Figure 25. Normal consolidation curves from oedometer tests for: a) Material 1, b) Material 2 and c) Material 3, and different densities.
The reference oedometer modulus, Moedref, have been evaluated at the reference stress of 100
kPa for all normal consolidation curves and is presented in Table 10. To be able to reproduce the normal consolidation curves or to calculate Moed for any normal stress, the stress exponent,
