Concrete behaviour under compressive loading: experimental research

Concrete behaviour under compressive loading

Citation for published version (APA):

Geel, van, H. J. G. M. (1995). Concrete behaviour under compressive loading: experimental research. (TU Eindhoven. Fac. Bouwkunde, Vakgr. Konstruktie; Vol. TUE-BKO-9502). Technische Universiteit Eindhoven.

Document status and date: Published: 01/01/1995 Document Version:

Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.

• The final author version and the galley proof are versions of the publication after peer review.

• The final published version features the final layout of the paper including the volume, issue and page numbers.

Link to publication

General rights

Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain

• You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:

www.tue.nl/taverne

Take down policy

If you believe that this document breaches copyright please contact us at: openaccess@tue.nl

Elndhoven University of Technology Department of Structural Design And Engineering

CONCRETE BEHAVIOUR UNDER COMPRESSIVE LOADING

Experimental research Part I: Survey of literature

Report BK095.02 January 1995 ir. H.J.G.M. van Geel

Contents

Contents 1. Introduction

1.1. A historic view

1.2. Research at TU Eindhoven 1.3. Aim of the present survey

2. Crack growth, volume change and stress-strain behaviour 2.1. Uniaxial tests 2.1.1. Pre-peak behaviour 2.1.2. Post-peak behaviour 2.2. Multiaxial tests 2.2.1. Pre-peak behaviour 2.2.3. Post-peak behaviour 2.3. Keywords for chapter 2 3. Test equipment 3.1. Introduction 3.2. Loading platens 3.2.2. Uniaxial tests 3.2.3. Multiaxial tests 3.3. Nonuniformity of deformations 3.4. Keywords for chapter 3

4. Stress path variations

4.1. Proportional versus non-proportional stress paths 4.2. Damage from previous loadings

4.2.1. Cyclic loading

4.2.2. Loading-rotation-loading 4.3. Keywords for chapter 4

5. Specimen size and composition 5.1. Specimen size

5.1.1. Pre-peak influence 5.1.2. Post-peak influence 5.2. Maximum aggregate size 5.3. Initial anisotropy

5.4. Concrete composition 5.4.1. Uniaxial tests 5.4.2. Multiaxial tests 5.5. Keywords for chapter 5 6.Summary 3 3 3 4 5

5

6 7 9 9 16 20 21 21 22 22 26 30 31 32 32 35 35 39

40

41

41 41 43 47 47

48

49 52

55

56

Introduction

1.1. A historic view

A first attempt to obtain experimental data on the behaviour of concrete under multiaxial compression was made by Fopple [l], at the end of the 19th century. Although restricted in terms of experimental means, he was able to point out some aspects of concrete behaviour under compressive loads which are still subject of research at the moment, almost 100 years later.

From this start up to the sixties research mainly focussed on the ultimate load bearing capacity of concrete, regardless deformational behaviour and microprocesses in the material. Most of the studies were intended to obtain information about the relation between multiaxial and uniaxial compressive strength of concrete. Only few researches tried to relate the observations made on a macroscopic scale to processes taking place at smaller scales. The work of Richart, Brandtzaeg and Brown is a well-known example of early work [10,11] dealing with microcracking.

From 1960 research on concrete behaviour accelerated enormously. Main causes of this development were the improvement of testing equipment and measuring techniques (caused by technological developments in general) and the growth of concrete applications (increasing the need for a fundamental examination of concrete behaviour) and -from the seventies on- a closer cooperation between different research institutes. At Cornell University overlapping research projects (p.e. Hsu et al., [100], Slate et al., [103]) were started in which both macroscopic and microscopic phenomena of concrete behaviour were investigated, providing fundamental insight in general aspects of concrete behaviour. However, although in the 1960's and 1970's the research on concrete in compression was extended in many ways, few investigators were concerned with the behaviour in the post-peak region.

It was not before the early 1980's that research projects were started inclosing systematic investigations on the post-peak behaviour of concrete under compressive loads. In section 1.2., the research conducted at the Eindhoven University of Technology regarding post-peak behaviour of concrete under compression, will be described. In this survey an emphasis is laid on this research.

Of course, experimental research can not be discussed without taking a look at numerical investigations. The increase of numerical possibilities in the last decade has led to a drastic decrease of the number of experimental research projects. More and more experimental results have become 'food' for numerical methods. The numerical aspects of concrete research can be found elsewhere and will be omitted in this part, unless needed to give insight in the subject

1.2. Research at TU Eindhoven

Since 1980 research has been carried out at Eindhoven University of Technology on the post-peak (softening) behaviour of concrete under compressive loading. Van Mier (1980-1986)

apparatus, developed at TU Eindhoven. More basic parameters were investigated both experimentally (with uniaxial tests in the same loading apparatus) by Vonk (1988-1992, including numerical research) and Stys (1993), providing fundamental knowledge about the subject

At the moment, a 'parallel project' is being carried out as a continuation of the work done by Van Mier and Vonk: on the one hand an experimental research, on the other hand a numerical investigation, attempting to develop a numerical model for concrete behaviour under compression that can be used in daily structural practice. The two research projects are carried out respectively by Van Geel (since 1993) and Bongers (since 1992).

1.3. Aim of the present survey

This survey intends to give an overall view on the behaviour of concrete under compression,

with an accent on experimental research aspects. It has no intention to be complete, although an exhaustive reference list on the subject is included and the most important researches are discussed in the next chapters. Thus it can be used as a reference by researchers who are familiar with the subject or as an introduction by those who are not

The reference numbers of books, papers and other publications (put in square brackets) refer to part II of this report ('Concrete behaviour under compressive loading - Experimental

research. Part II: Bibliography 1900-1994'). The author acknowledges the work done at TU

Eindhoven by dr.ir. J.G.M. van Mier and dr.ir. R.A. Vonk, which made writing this survey much easier.

2. Crack growth, volume change and stress-strain behaviour

Concrete is a composite material, consisting of cement, gravel, sand and water. After hardening of this composite material the material can be regarded as a mortar matrix including distributed aggregates. Although both the mortar and the aggregate material (sand/gravel) show a more or less linear stress-strain relation and very brittle behaviour after reaching the ultimate load, concrete -as a composite of these two- shows a nonlinear stress-strain relation, even at very low loads, and after reaching the peak load a descending branch in this stress-strain relation, called softening [ 445]. This difference in stress-strain behaviour appears to be caused by microcracking.

2.1. Uniaxial tests

The first observations on the influence of microcracking on the stress-strain behavior of concrete under compression were done by Richart, Brandtzaeg and Brown [10, 11], and later by Jones [25], L'Hennite [28], Hognestad et al. [34] and Rtisch [66]. They recognized that the shape of the stress-strain relationship was related to irreversible (micro)cracking. But it was not before the 1960's that at Cornell University direct observations were carried out on concrete sections to detect the nature of these microcracks (Slate and Olsefski [103], Hsu et al. [100]).

In concrete, there appear to be three different types of microcracks: 1. Cracks running through the mortar matrix;

2. Cracks running through the aggregates;

3. Cracks at the bond between mortar and aggregates.

([33, 100, 103, 135, 183, 286, 397] and many others). Cracks running through the aggregates are for example found in high-strength concrete (Carrasquillo [370]). The interface between aggregate and mortar has a different structure ([520, 534]) and forms the weakest link in concrete.

Carrasquillo concluded from his findings that it would be more appropriate to divide microcracks in only two different types [370]:

1. Simple cracks: isolated bond or mortar cracks;

It has been shown that microcracks already exist before any load is applied to the concrete ([103, 133, 183, 293] and others). Most of these pre-existing cracks appear to be bond cracks. The amount and location of these microcracks seem to be dependent of the type of cement, the mineralogical nature and the geometry of the aggregates, the water-cement ratio and the curing conditions (volume changes due to hydratation, bleeding and shrinkage) (DiTomasso [ 452]).

2.1.1.Pre-peak behaviour

Spooner indicated [314,326] that fracture of concrete in compression is a progressive process. By comparing acoustic emission experiments with an 'energy-dissipation-model' for an ideal material, he concluded that damage starts at very low strain-levels and leads to failure in a progressive way. More about Spooner's research can be found in chapter 4.

Brandtzaeg was the first to recognize that the joining of microcracks into continuous crack patterns, according to Brandtzaeg at about 70-90% of peak-load, was accompanied by a

reversal point in the volume change-curve. This was later confirmed by Hsu et al. [100],

Krishnaswamy [ 183] and others. Brandtzaeg defined the stress at the minimum volume point

as the 'critical stress' (see also [36, 79, 168, 179, 193, 230, 354]). In table I some

experimental results are gathered.

Table I: Microcrackin~ and critical stress in uniaxial tests (after Van Mier [399})

Loading at which critical stress measurement

microcracking starts

Krishnaswamy 30% of peakload 70-90% measurement of

microcrack length

Hsu et al. 30% 70-90% measurement of

microcrack length

Sturman et al. 30% 70-90% measurement of

microcrack length

Desayi and

-

77-85% strain measurements

Viswanatha (cylinders)

Riis ch 50% 75% ultrasonic testing

l'Hermite 50% 75% ultrasonic testing

Beres

-

50-80% strain measurements

(prisms) The long-term strength of concrete is often related to this critical stress. At higher stress levels

instable crack growth occurs. This means that more energy is released by formation of cracks .

than is needed to procure failure: cracks are able to grow without load increase (Slate and Hover [473]).

Carrasquillo [370] examined crack formation in low, normal and high-strength concrete using

X-ray films and concluded that the stress-strain behaviour in uniaxial compression was directly related to the observed internal process of microcracking. The X-ray photographs of crack

surfaces were taken at several stages in the stress-strain curve. Also measurements of volume change and Poisson's ratio were considered to be appropriate tools for prediction of the critical stress point, which was found to be between 76 and 100% of the ultimate load, depending on the type of concrete.

2.1.2. Post-peak behaviour

Very few experiments on the post-peak (softening) behaviour were performed before the end of the seventies. The main reason for this absence of experimental research was the difficulty of obtaining a stable softening branch. Load-controlled test equipment is not capable of measuring a post-peak descending branch: Loading beyond peak stress leads to an uncontrolled, sudden failure. Researchers tried to solve this problem in various ways, for example loading a steel tube parallel to the specimen, which could absorb the energy released after peak stress (Wang et al., [352]). Even in displacement-controlled tests precautions have to be taken to guarantee a stable descending branch.

In [350] Sture and Ko gave a schematic description of the stress-strain behavior of a fractured rock specimen (fig. 2). Softening of brittle geologic materials like rock had been observed earlier by Bieniawski [157,198] and others.

In the stress-strain curve point A represents the peak stress. Fracture is assumed to take place in three different failure modes: shear, 'tensile multi-fracture' and a combination of these two. After peak stress the material can no longer be regarded as a continuous homogeneous material, but as a heterogeneous granular structure. Softening takes place only in the '.joints' (shear bands) while the rock masses outside the shear bands continu to behave elastic (points B and C). Thus, the softening response seems to be a structural rather than a material property (see also 157). When the residual stress is reached (point D) further granulation of the material does not affect the strength parameters significantly.

~ <C >< < P(.Atc S";"R:£t.c.TH EtNEL.OPE t @ O'"

~'

k-£:=

'"~·

/

®

I

-'

/t

®a•cs1o"AL

JI' (RES I~"

er

~k

AXIAL STRAIN

Kotsovos [429] carried out uniaxial compressive tests with different testing techniques. In the experiments concrete cubes (100 mm) and cylinders (height 250 mm, diameter 100 mm) of two different strengths were tested at a displacement rate of 2.25 mm/hour. Because Kotsovos was mainly interested in the effect of the boundary conditions on softening, further discussion of this research will be given in chapter 3.

In 1984, Van Mier carried out some uniaxial tests, mainly to obtain information about the influence of some manufacturing parameters and the effect of specimen height (see chapters 4 and 5) on softening behaviour [466, 508]. The tests were performed on 100 mm normal strength concrete cubes at a loading rate of 5E-6/s or lOE-6/s (strain rates).In fig.3 typical stress-strain measurements are shown, in which the axial stress is plotted against overall strain ·

measurements (between the loading platen) and surface strain measurements (strain gauges). While the overall measurements result in a descending branch, the surface measurements indicate unloading at the specimen surface. Van Mier concluded from this that the residual load bearing capacity (post-peak) is a result of a 'more or less' intact specimen core (See also Kotsovos [ 429]). ~ "' c c -70 -60 -so .... -to z ;;; ·20 ·10

~JAi-i SI-El tLOA .PL. 1

Go <DJAl-1 51-(1 ( SURf.' ...__..3F'1-2 Sl-[HLOA.Pl. 1

._ · ·•JAl-2 51-[)(SURr .1

~3Al-3 51-[ltLOA.PL..J

.._ .... JAl-3 St-[t(SURr. •

SUESS St vs. ")fRArN [lflOA.PL. 'SURr.'

8RICH1'RISn• JAi

LOA.rans. ")1/S2/S3:-1/DIQ

LOA.~EGfn(. MONO IONIC

PERP(NOICUi.AR

(a.)

0+--+~-+-~+---+~-+-~-+-~1---+~-+-~f---+~~

0 ·I ·2 ·3 -4 ·5 ·6 -7 -8 ·9 ·10 ·I I -;2 SJRAIN (PSI 1 l ll'..J

Figure 3: Uniaxial stress-strain curves, surface and overall measurements (Van Mier [466])

Based on these tests Van Mier concluded -like others mentioned above- that a structural response rather than a material response was being measured in the post-peak region stress-overall strain behaviour.

Tests on prisms (100x100x200 mm) by Van Mier showed a similar difference between overall and surface strain measurements, but in these tests the fracture of the specimens was not as gradually distributed through the specimens as in the cube tests. A localised "shear-plane" was observed in several prism-tests. This failure mode was attributed to non-uniform stress distributions within the specimen (see also Newman and Sigvaldason [149]), caused by rotation of one of the loading platen and the non-homogeneity of the concrete specimen. This

kind of shear fracture was also reported by others, for example Kotsovos [ 429] and Vonk [606]. An important observation was made by Van Mier comparing both the distributed and the local failure modes: no influence of the mode of failure was found on the macroscopical stress-strain curve.

More experimental research on the phenomenon of localization of defonnation in shear bands has been carried out by Torrenti et al. [513, 566, 598], using several advanced measuring techniques. Stereophotogrammetry was the main measuring technique, which made it possible to make defonnation maps of the specimen at several loading stages. The tests were carried out on l 20x30x60 mm prims, two made of plain concrete and one of fibre reinforced concrete. Their method clearly showed the localized fracture mode. Another important observation in the tests is that localisation starts already before peak stress. Torrenti, just like Van Mier, favours a stress-displacement curve for the post-peak behaviour (instead of a stress-strain curve).

-·-·-~I~~ \ _{•' \}

-·-·-·Jl.

Figure 4: Shear-plane fracture in uniaxial tests (Van Mier [466])

Uniaxial compression tests on high-strength concrete on softening behaviour were carried out by Taerwe [597, 611]. The test specimens were cylinders with a diameter of 155 or 192 mm and a height of 380 or 483 mm, and a compressive strength of approximately 90 MPa. The control parameter in the tests was a combination of the axial and the circumferential strain (see also Shah, Gokoz and Ansari [405], and Glavind and Stang [583]), measured by the movement of a thin steel spring wrapped around the specimen. Taerwe also observed a localized shear band fracture mode and concluded that the fracture aspect in the experiments carried out is very similar to that in normal strength concrete. The shear band is the result of connecting microcrac.ks, that start at a very localized zone at the specimen's surface.

2.2. Multiaxial tests

2.2.1.Pre-peak behaviour

As in uniaxial tests, several researchers started looking for a relation between volume changes, microcracking and the stress-strain relation in multiaxial tests. Dependent of the amount of

and strain. At peak stress very large strains can occur, indicating a highly deformed specimen. Furthermore, when the level of confinement increases, the maximum load increases.

Krishnaswamy [183] explained this by a 'slow-down' of rnicrocracking due to this

confinement (see also Robinson [166]). However, at about 80% of peak stress, the amount of

microcracking seemed roughly equal to the amount measured in uniaxial tests. Unfortunately,

Krishnaswamy only studied microcracking in tests performed with 'dry' loading platens.

In figure 6 some stress-strain curves obtained at Imperial College (Newman [363]) are shown,

from which it is obvious that peak stress and strain increase with increasing confinement

. . . .

.

"·

..

·

..

,

~· I 0 I • ·'" . . I ,, .c •• •.. C-4 ·, ... ·. ·,,. . ,· .. •• c J J . 0: , ac •· .. . • • • • ' GI ' . 0-5 !J-6 0-9

Figure 5: Localization of deformations, distorsion map evolution (Torrenti [566])

C .. ,

,

,, ..

~ N/mm•

Ii

G • 0 8 ) ~ c ~ e o 1> a E n ~ F 1&. 7 H,G 69 0 J .i< 1)8 ) -15000 - 100000

"°" ... " -

50000 A _S<XXlO

Newman [363] gave a comprehensive overview of the work done at Imperial College. In this overview he distinguished three transitions observed in the multiaxial stress-strain behaviour of concrete:

1. 'Initial cracking'. Below this transition (i.e. stress level) - at about 40-50% of peak

load-concrete behaviour is similar in loading and unloading. Earlier [336], Kotsovos and Newman called this transition the 'onset of stable fracture propagation' (OSFP). In the Rendulic plane

(at Imperial College all tests were performed using a loading apparatus in which the two

confining pressures were equal) the initial cracking envelope closes in on the hydraustatic axis

at increasing lateral stress. According to Newman this effect could be explained by the occurrence of stress and strain concentrations within the specimen and the collapse of the cement paste phase.

2. 'Final breakdown'. This transition corresponds to the minimum volume change point in the

volume change curve. Whereas the initial cracking transition was related to the fatigue strength of the material, the final breakdown transition was associated with the long-tenn strength (as in the uniaxial tests described in the previous paragraph), and was called OUFP ('onset of unstable fracture propagation') previously by Kotsovos and Newman [336].

3. 'Ultimate'. This stress level corresponds to the maximum bearable load, just beyond the

final breakdown stage. In figure 7 the several transition curves are shown in the Rendulic

plane.

Figure 7: Transition envelopes defined at Imperial College [363]

A similar classification was made by Launay et al. [221, 242], who distinguished a 'discontinuity limit' (similar to the OSFP) and a 'failure level' (compare with OUFP). A graph similar to figure 7 was obtained.

In general it can be stated that in multiaxial tests the critical stress level (and thus the minimum volume point) occurs at relatively higher stress levels than in the uniax.ial case.

In figure 8 the triaxial failure envelope found by Nojiri [ 468] is presented. Note that the tenns

a1<0'2=0'3 (compression is negative), leading to a relatively distributed crack pattern, and

0'2=0'3<0'i. resulting in a quite localized (more brittle) failure mode.

Gi/fc -1.0 Compressive meridian -1.0 -2.0 -3.0 -4.0 .J'l Uz/fc = .J'l

aJ/

fc

Figure 8: Failure envelope found by Nojiri [468)

A special case of multiaxial tests is the biaxial compressive test. While the maximum bearable load is increased due to the lateral confinement in the intermediate principal direction, failure is

stimulated in the minor principal direction because of the specimens possibility to deform freely in that direction. In these biaxial tests always a very brittle failure mode is observed, showing a highly localized crack pattern. Because of this brittle behaviour few biaxial tests have been carried out including post-peak behaviour. In figure 9 some biaxial failure envelopes are shown. For examples of biaxial tests see for instance Nelissen [223, 263], Kupfer [275], Liu et al. [262], Gerstle et al. [344] and-including post-peak behaviour- Van Mier [466, 508].

J 'l\ ~I '" \ \

.

\ I I I I I \ I / / -QB I I / ·~ ' I / ' ::::. O' ,, .>. ·i ' / / /

b1,.,.1 rtsults urin SAIS8/6A

• • Q-201-10

I

o • 0.0 /-10 t.lrtu-rato g : -0.Jlt-10 0210, • • Q.O t-lD 6t.pt -r1tio •~ n201-10] '•-OJJ/-tO l12 1 U11 - 0 2 1 0 , . 1 1 OSO 0.7S tO 1.2S lSO

=

l("phr ~: ~~=~~ pl•ft' lOO•ZOO•!IOMIJ llnAMI ---lut'lal. '.(•11-JSNJ-:Zpi:.11t' 127•127•12.7IMlll) llnntws · - - · TUtl r·

•)1]NJ--- 9AM JH

-·- cu 190

In general in biaxial tests the same transition stages have been observed as in other multiaxial tests.

Van Mier [ 466, 508] carried out a large number of triaxial experiments, in order to obtain data for numerical simulations in both the pre-peak and post-peak region. In this experimental research 'true' triaxial tests were carried out on concrete cubes, with independent stress-deformation regimes in three directions. A photograph of the loading apparatus is shown in fig.10.

Figure 10: Triaxi.al loading apparatus developed at TU Eindhoven

Four parameters were studied in the test program: 1. Influence of loading path (see chapter 4);

2. Influence of the confinement in the third (minor) principal direction; 3. Influence of orientation of the initial damage field (see chapter 5) 4. Influence of cyclic loading (see chapter 4).

Loading of the cubes (100 mm) was applied following different stress and displacement paths. The maximum aggregate size was 16 mm, the water-cement ratio 0.50 and the cement used was Portland cement type A, 320 kg/m3• In fig.11 and 12 two graphical representations of the

failure envelope, determined by Van Mier, are plotted.

A good agreement was found with the results of Liu et al. [262], Kupfer [275] and Gerstle et·

al. [344]. In fig. 13 two examples are presented of stress-displacement curves obtained by Van Mier.

50 ·•I e '

:-

i

lO 0.1 / - 0.1 / / 0.

.

a 0

.

-1.0 Ci3I01 l)ar~. 0.10 e:!r,!! . 0.10

...

.

O.OI prrp. O.GI / / / ·)' / ~'\ -1.I -2.0 v₂ !mm!

Figure 11: Failure envelopes by Van Mier (I) [508]

... E .!: z - -1SO 0 -100 -SO - - - - POOCiORSKI 5 parameftr model - 50 11 tic , 0.08 ; le' 46.6 N/mm 2 C₀,0.08fc; _C1: 1.402; (2' 0.321/lt -100 experimenh • series 516. •series S/9, ~'O.OS x s.r ies 8/9, ~ = 0. 10 -150 -200 stress 02 r ti/mm 21

10 i.s io ts 10 - Imm! UJ

---- 982 .. 4 10) I 01.: 0.'01 - - 9A2·0. lo1 to1 a0.0~

- s,t.1. 3 10₃101 a OJ .S 0 ·.S -tll -15 -lC ·l.S ·lO 0 -.5 -10 -15 -10 -25 -10 CJ;--etflt-S Sl·U -1111t·S &t-U --111111·~ Sl-[l 30 25 tO II I su1css-s1111111• <lll'•ts srocn "· rnrn -HO -100 ('SCI> n,.J :~~~~~:: 11ffit LOll.(Of'll . .11 52/Sh •0.11-1.1 SllSla •0.11•1.0

LOll.~(Oln(• "°"OIOlllC 'tl'[ .. OICULAR

h.I

•i ·10 ·II • 0 • I • 0

Figure 13: Stress-displacement curves for triaxial experiments, left ''plane-strain" test (u'2==0), right constant stress-ratio experiment (Van Mier [466])

Like in uniaxial compressive tests (paragraph 2.1.) Van Mier observed the formation of a localized shear zone, but this zone could be detected more easily than in the uniaxial tests, because of the reduced effect of the boundary conditions (see chapter 3). Two clearly different fracture modes were distinguished by Van Mier:

1) Planar failure mode: A pronounced sh~ar band fracture mode ( a clear localization of deformations), occurring when a preferential direction of failure was present (two different confining stresses or "plain-strain" tests in which the deformation in one direction is

completely prevented). This means the presence of one large tensile deformation.

2) Cylindrical failure mode: A more distributed fracture mode, which is the result of mutually crossing shear bands, occurring in stress regions near the compressive meridian (equal lateral confining pressures). Uniaxial compression is also a loadcase in this region. This means the presence of two large tensile deformations.

Planar mode failure is a more brittle failure mode, the cylindrical mode a more ductile failure mode. In both modes shear bands developed in planes where a large compressive displacement occurred together with a large tensile displacement In fig. 14 a classification of failure modes by Van Mier is given.

Van Mier concluded that the concrete pieces between the shear bands are almost uncracked (compare with Sture and Ko [350]), indicating unloading of these pieces as the deformations localize in the shear bands.

o,,

Le,

.l!ll\!:.!,_ (hid. 21 d•100mm

o,b_

~

. I £1 casting-1SAl-S I surtac• fh/d=OSJ uniaxial comr>n~ssion

.frlirdrical mode -~lanar mode

lriaxial c.omRression 01<°:2<03<0

Figure 14: Fracture modes classification (Van Mier [466))

2.2.2.Post-peak behaviour

The first true triaxial tests including post-peak behaviour were carried out by Van Mier [ 466,

508] at TU Eindhoven. Parameters studied and materials used are described in the previous

chapter. Van Mier, when evaluating the stress-strain behaviour, made a distinction between the influence of the minor principle stress and the intermediate principle stress. Furthermore the behaviour under tension-biaxial compression loading was examined.

The influence of the minor principal stress was observed in "plane strain" tests (£2=0), in which the minor principle stress was varied (0, 0.05 and 0.10 times the major principal stress, respectively). An increase in confining stress 0'3 results in an increase in peak strength and strain (cr1-E1) and a decrease in the rate of increase of lateral deformation (£3). The shape of the descending branch is similar for the applied confined stresses {though the residual stress level increases with increasing confining stress). Failure is mainly restricted to the 1-3 plane.

The decrease in 0'2 after peak stress indicates unloading in the 2-direction. This results in Van

Mier's planar failure mode (pronounced shear bands, see previous chapter). See fig. 13 Oeft).

The influence of the intermediate principal stress was investigated by applying a constant minor stress 0'3=0.05*0'1 and varying the intermediate stress 0'2 (0, 0.1 and 0.33 times O'i.

respectively). See fig. 15.

Two conclusions were drawn from these results. First, there appeared to be a good agreement

between test 8B2-4 (fig. 15) and the plane strain tests (fig. 13, left), indicating that there is no difference between stress or strain-ratio tests (see chapter 6). Second, where the softening

branch of experiments 9Bl-3 and 8B2-4 are relatively steep, the descending portion of test 9A2-4 is deviant The gradually descending curve is the result of two relatively large tensile deformations leading to Van Mier's cylindrical failure mode.

From the tension-biaxial compression. experiments Van Mier concluded that the energy-requirement (surface under the O'-E-curve) was about the same as obtained from uniaxial tensile tests (remark: a very limited number of experiments were carried out in this stress region). -120T

_JI

'°

1 1Nlmm21 , ..

--

... , -80 ,, ' I ' '

.

, \ I / / \ \

,,.

..

\ \ 30 2S 20 1S 'll S 0 -S -10 -15 -20 -2S -30

- - str1in Ezl,.. .. J -100 strain E 1

f'Y.o)-.--···--, eol;;:;

,,,,"'

"'\

-

!

, / / _{\ _60} ~ - ·- 981-3 <-1/-0.0SIOJ , ' - - 9A2-4 1-1/-0.'lli-0.0SJ -- / " ---- 882-4 (-1/-0.33/-0.051 - - -- -40~

- -- · - - · - -:; loading df"ectioo: parall~

-20

~ ~ 20 ~ 'll 0

- - •lnin E) (%.)

Figure 15: Stress-strain curves for experiments with varwus intermediate stress (Van Mier [466])

Van Mier also related the volume change of several tests to the observed stress-strain and failure behavior, see fig.16, in which the strain in the major principle direction for both planar and cylindrical failure modes is plotted against the volumetric strain. The cylindrical failure mode showed larger volume-increase after peak stress than the planar mode. In both failure modes a minimum volume was observed just before peak load. The minimum volume was reached at lower values of the strain in major principle direction. The volume change curves appeared to be closely related to the distinguished failure modes.

Investigations on the influence of confining pressure on the post-peak behaviour of concrete were performed by Jamet et al. [458]. Triaxial tests were carried out on microconcrete cylinders (diameter 110 mm, heigth 220 mm) with the following admixture:

sand 2.5-5 mm: 1180 kg sand 0.8-2.5 mm: 275 kg sand 0.2-0.8 mm: 415 kg cementCPA55: 340 kg water: 1801

!"lt=IJOR COl"IPRESSIY( STRAIN (I YS. f'OLUl"l(TRIC STRAIN ·JO CONSTANT STRESS-RATIO _{SJ/SI = -0.10/-1} ri:srs .I') LO~O I NO PRR~LL(L ..._.SA2-2 MONO -24 ; . ~:~~ ~~~~ S2/SI: Q.l').'-1-0 52/SI: -0. 1/-1.0 S2/S1:-0.JJ/-1.o -22 • =;Ax ... ~LUE or SI -20 I -1 S f -12 _{fig. b.)} -10 -B _,. 5 -s -2 .s 2.s s 7.S 10 12.s IS (-VOL 14.1

"RJOR CO"PR£SSIV£ STRAIN Cl VS. <OLU"£TRIC STRAIN ·JO

-26 -26

CONSTANT STR(SS-AATJO TESTS sJ1s1 :r. -o.os1-1.o

LOAOINO .-AltALLCL

....__..9Bl-3 CYCL 52/SI• Q.l')/-1.0

-24 ... +9A2-4 MONO 52/SI: -0.1/-l.O

cg.· .[1882-il CYCL S2/Sl:-O.J3/-1.0 -22 .. :; nAx. "iALU( or SI -20

...

,.

·"

J8 ¢:12 _{fig. a.)}

•

-10 !fl ' di ~ ' llJ i -6 /J;I ~ _, .5 -5 -l. 5 z.s s '-5 10 12.s is (-VOl C't..J

Figure 16: Volume change curves for triaxial tests (Van Mier [466])

er, -a3 [N/mm2_] a₃ = -100 N/mm2 -150 a3 = -50 N/mm2 -100 a3

=

-25 N/mm2 -50 a3 = -10 N/mm2 a₃ = 0 N/mm2 a3

=

-3 N/mm2 OL--"'~~~~~~~~~-0 -25 -50 -75-100 c,[:~q £3[%.] 75 50 25 0 0 -25 a₃ = -3 N/mm2 Oj

=

-10 N/mm2 a₃

=

-25 N/mm2 a3

=

-50 N/mm2 a3 = -100 N/mm2

-so

-75 -100 t:,[%.]

Figure 17: Influence of confining pressure on stress-strain behaviour and lateral deformations (Jamet [458])

These graphs clearly show the influence of confining pressures. At confinement levels up to 25 MPa softening-behaviour was observed, at higher confinement levels hardening occurred. This

behaviour is reflected in the fracture modes: for confining pressures up to 10 MPa 'open fractures' (shear bands) were observed, at a confining pressure of 25 MPa specimens showed a more smeared fracture pattern, at higher confinement levels no visible damage could be detected at all. The transition from softening to hardening behaviour caused by increased confinement is usually referred to as 'brittle-ductile transition'. Vonk [606] states, considering the residual stresses in fig.17, that not only crack formation but also aggregate interlock and friction play an important role in softening behaviour, due to which "shear cracks have a significant mechanical resistance when a confining pressure is applied" (see also Walraven [385]).

Hurlbut [514] carried out further investigations on the brittle-ductile transition of concrete under triaxial compression. Normal strength (22.1 MPa) cylinders (cement:sand:gravel =

1:3.16:3.19, max. aggregate 10 mm, water-cement ratio 0.833) with a height of 152 mm and a diameter of 76 mm were loaded first in the lateral directions (cr1=0'2) up to a certain stress. Then this lateral stress was kept constant and the axial stress was increased (0'3).

Smith et al. [564] carried out standard cylinder tests in a triaxial apparatus to obtain information about the following aspects:

1. Maximum strength, residual strength, and transition point between brittle and ductile behaviour under triaxial compression;

2. Plastic strains and volume change at peak and in the post-peak range; 3. Instability phenomena at failure;

4. Effect of concrete strength on some of the preceeding phenomena (see chapter 4 ).

The specimens (51 in total) were 54xl08 mm cylinders of low and normal-strength concrete (34.5 and 44.l N/mm2) with a ratio cement:sand:gravel of 1:3.16:3.19 (water-cement ratio

0.833). In fact, these are the same ratios as applied in Hurlbut's experiments. Also the same loading path was followed as in Hurlbut's test to make a comparison possible. In addition, a 'multistage stress path' was adopted to explore the influence of load history. Control parameters in the test set-up were both axial displacement and lateral pressure, in order to obtain a stable descending branch in stress-strain curve. In fig.18 results of tests with different lateral confinement are presented. The plots are qualitatively similar to those by Jamet.

Fig. 19 shows the increment of plastic volume strain plotted against axial strain for both a confined as an unconfined test. Both experiments show a compactation in the inital phase, but -while in the unconfined test at relative low axial strain a zero volume change is observed followed by rapid dilatation near peak; decreasing in the post-peak range- the confined test shows a much larger compactation range with a zero volume change at high axial strain, and much less dilatation. Smith et al. concluded: "If dilatation is a sign of damage to the concrete, it follows that the concrete under high confinement has suffered less damage than the unconfined concrete."

SIG 1 .. SIG 2 • S.O kSI •.o 3.0 2.0 1.0

·'

.1 0 -10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 B 9101112 EPS-3/EPS-0 EPS-1/EPS-O

llRITllHJLCTILE T!UNSITIC»I: 5 KSI CONCRETE

Figure 18: Stress-strain curves at several confinement levels (Smith [564])

...

.

.

•

..

.

z 1.2

'

! " I o.o !! o.• ~ _o.• A ~ 0.2 ~ -0.2 -0.4 -0.6 -o.e 0

INCREMENTAL PLASTIC VOLUME CHANGES

-10

UNCONflNCO ANO l 1<$1 CONf\NCMCfT

-20

CPS-l (s 10-l tN/lN)

->o

Figure 19: Plastic volume changes for confined and unconfined compression (Smith [564])

2.3. Keywords for chapter 2.

In part II (Bibliography 1900-1994) a global keyword index is included (page 4). To find more

information about the subjects discussed in this chapter, try the following keywords:

- Uniaxial tests

- Multiaxial tests I biaxial tests I triaxial tests.

- Fatigue tests I long-term loading I sustained loading.

- Failure theories I models I fracture mechanics I constitutive modelling.

3. Test equipment

3.1. Introduction

From research, mentioned in the previous chapter, it is known that the softening (post-peak) response of concrete is rather a structural response than material behaviour and is therefore highly dependent on the test environment. 'Test environment' in this sense is:

1. The layout of the loading apparatus;

2. The stiffness of all parts of the loading apparatus;

3. The amount of shear stresses introduced by the loading platens.

Researchers at TU Munich studied the influence of the layout of the testing device exhaustively (note that 'triaxial' loading devices, in which the stresses in all lateral directions are equal, are not discussed in this chapter) and developed a 'multi-part' loading apparatus, i.e. an apparatus in which the three loading axes are able to move independent of each other and hence minimizes additional shear stresses at the specimen surfaces (especially in the softening regime) and a non-symmetric defonnation of the specimen can be avoided, problems to be dealt with in a 'one-part' loading apparatus (fixed axes). See for example Linse [346] and Winkler [492]. These problems, which can influence the observed concrete behaviour significantly, were also recognized by Van Mier [ 466] in the case of the Eindhoven loading apparatus, in which the vertical axis is completely fixed in the axial direction. See figure 20. Both loading equipments consist of three hydraulic jacks. Another possibility to overcome abovementioned problems is to make use of six hydraulic actuators (two per axis), but this option is less favourable from a financial viewpoint

al 1. ti•,. 6•2· 1j>l•1•2l 2. 612.ti•, . .Plr1•2l . ...ll hud bl I 1'1 , , I --f"'-•--- < ~· -I j "' I J 1₂ -~---- ~~fcrnwd cube ~. t.1,.6•2 .,..,.,.Irie ! _{& 3} non·symme1ric I

Figure 20: Left: Non-symmetric deformations of a concrete cube iri the Eindhoven multiaxial

Of course it is impossible to construct a 'perfect' multiaxial loading apparatus because some kind of disturbing effects will always occur (for example, when using pulleys to suspend a loading axis, stick-slip- or frictional effects can not be excluded completely). However, it is preferable to approach 'true triaxial loading' as close as possible, but most of all it is necessary to understand the limitations of a loading apparatus and to be able to estimate the effects due to the layout of the apparatus.

In the following paragraphs, the influence of the friction at the contact between specimen surface and loading platen (§3.2.) and of the rotational stiffness of the loading apparatus (§3.3.) are discussed.

3.2. Loading platens

To introduce the compressive load at the specimen surface, in the past several loading platens have been developed. Initially nearly all loading platens consisted of normal 'rough' steel platens. Later it became clear that the shear stresses, introduced by these platens at the contact between specimen and loading platen, had a major influence on the observed concrete behaviour and other loading platens were developed to eliminate these frictional effects as much as possible. The most common platens used are:

1. 'Dry' (or 'rough') steel loading platens. These platens were for instance used by Weigler and Becker [106], Krishnaswamy [183] and more recently by Torrenti [566] and Taerwe [697]. Nowadays these platens are mostly used for comparative reasons.

2. Platens with intermediate layers. To eliminate friction at the contact surface several intermediate layers have been used, like chalk (sometimes with aluminium foil) by Kobayashi and Koyanagi [260], thin metal sheets by Erdei [375], teflon sheets with bearing grease by Vonk [606], multiple layers (grease, teflon and aluminium sheets) by Murakami et al. [623], etc.

3. 'Brush' platens. These platens, developed by Hilsdorf in 1965 [126], consist of a large amount of small steel rods assembled in a package. These loading platens have been used in some of the most important researches into the behaviour of concrete under multi.axial compression, like Nelissen [223], Kupfer [275] and Van Mier [466].

Other loading platens have been used, like fluid cushions (see paragraph 3.2.2.), but will not be discussed further.

Besides the friction introduced by the loading platens the rigidity of the platens needs to be considered. See figure 21. Infinitely rigid platens lead to a constant axial displacement at the specimen surface, weak platens lead to constant axial stress along the boundary.

3.2.1. Uniaxial tests

To obtain material data for analytical descriptions of concrete behaviour and implementation in numerical methods (FEM) it is not only necessary to obtain pre-peak data, but also post-peak material characteristics. The influence of loading platens on this softening behavior in uniaxial tests has been examined by Kotsovos [4.29] on concrete cylinders. Using two types of concrete (with cube strengths 37. 7 and 60 MPa), the following friction-reducing media were tested in uniaxial compression tests at a loading rate of 2.25 mm/hour:

T~o-4~oJ

I

tr= k¥nst.

I

~

Too

Cf

oar

Oh

I

e:

=k+s1.

I

I

Figure 21: Rigid versus weak loading platen (Van Mier [399))

1. No anti-friction medium (dry loading platen); 2. Synthetic rubber (0.45 mm thick);

3. MGA pad (0.008 mm thick hardened aluminium steel, grease and polyester film); 4. Brush platen (3.175x3.175 mm, distance in between 0.076 mm).

In fig. 22 it can be seen that in the pre-peak region the deformational behaviour is hardly influenced by the type of anti-friction medium. In the post-peak region however the softening branch becomes steeper when the frictional restraint is decreased. Based on these experiments Kotsovos concluded that -in the case of a complete elimination of friction- an immediate and complete loss of load bearing capacity would occur beyond peak stress.

,0

"

-1~ iliQ!2. Jc -N/,....I 0 AtUo-lts1:q"' ~ • so ·~ ... ~. " OCl~•"ll'Otl\I 8 po.n stfft ptat ....

C MGA pod ...a btofOtf'

0 Orvsh plOlfO'\

E MGA Pod mt uMd 0.-tri:w•

F '\.loc.>t '°""' ~-~--- -~-f-(a) • 1 · 0

-1-1LL:=I!-~-H-I 0 ih)

...

>O di

.

.

•

.,

... ..• ·~

.

.

.

..

,

•

.

.

...

_..,

..• ..•

_..

_,

.ill!!!2. ~ ~~"""""'°' ... ,-.... MG& P*' ~ f»torf - - br\Nh plOI.., - · - ·~ 1a.,.., Pu·I\. -..-..111,..IO,,_, IOGCl•l'l!Ocorr~ m.oOld•NllOt~I 10 . , ... · - · - ; OCI .... lftfrOtl\I - poor. " " ' , ... - - tw'Wtplol ... - · - ... io.,... - - - ..c;.APOOraC'--"~ 11r1.i.&u ....,,_..,..,~ l.S 0/6u b:ldarGOltf'_.~ OloOI01..-x".,-I

Vonk [606] agreed with Kotsovos on the fact that softening is highly dependent of the boundary conditions, but disagreed with Kotsovos' proposal for perfectly brittle post-peak behaviour, because a) the low-strength concrete in fig. 22 shows a distinguished descending branch even for low frictional restraint and b) the brittleness of Kotsovos' specimens was partly due to splitting forces caused by the soft interlayers.

Like mentioned in the previous chapter, Kotsovos also observed failure in shear bands and found that the inclination of the shear band was significantly influenced by the boundary constraint. When very low frictional shear stresses occured, the shear band became nearly parallel to the direction of loading {fig. 23 ).

Figure 23: Cylinder tests fracture modes, left lower strength and right higher strength concretes, in both pictures from left to right less boundary friction (Kotsovos [429])

Similar experiments were carried out by Vonk [567], both uniaxial and triaxial. The major difference with Kotsovos' tests was the use of a fixed loading platen instead of a hinged loading platen, to reduce the rotation of the loading platen when a macrocrack is formed which influences the final macrocrack failure mechanism.

Five different loading platens were used: 1. Rigid steel platen;

2. Teflon platen (with Molykote BR2 Plus grease);

3. Short steel brush (5x5 mm, distance 0.2 mm, h=84 mm); 4. Long steel brush (the same as 3 but with h=l 19 mm);

5. Hinged teflon platen, to investigate the influence of rotation of the loading platen when macrocracking occurs.

Test specimens consisted of normal strength (about 40 MPa) cubes with sides 100 mm. Special attention was payed to flatness, parallelism of sides and orthogonal surfaces of the test cubes. A loading rate of 1 µm/second in the uniaxial tests and in the major principal direction in the triaxial tests were applied. The two other axes in the triaxial experiments were force controlled with constant force ratio with the principle axis of 0.05 and 0.30, respectively.

In fig. 24 stress-strain curves are drawn for both uniaxial and triaxial results for different boundary conditions.

N

§

~ Z? GI ... iii -60 -50 -40 -30 -20 -10 0 .---.--~---. - - long bn.Jsl1 - 160 ---·dry platen -hing&d tefl. platen - · - teflon platen ~ -120 -E 6 -100 r1> -80

x

₀ en -60

.,

~ b _-40 en -20 0 ..

---

- Teflon ... _platen / _,...,.. ·" ··· Lono .. ·•· / ---·Short

/:>1\'

"'··"'"•

'

I ,;(.·· . \ - Dry pl a ten

//

\

\ \

f

\.

\

'

_'·

f

~-

..

: 0 -2 -4 -6 -8 -10 _{0 -5 -10 -15 -20 -25 -30 -35}

strain [o/oo] _{strain axis 1 [o/oo]}

Figure 24: Stress-strain curves for different boundary conditions, left uniaxial and right triaxial tests (Vonk [567])

Both Kotsovos' and Vonk's test results show that concrete in compression becomes more brittle when the introduction of shear stresses is limited. Also, from fig. 24, the effect of a hinged loading platen is evident: due to a large rotation of the loading platen as soon as softening starts, a much steeper descending branch was observed. The difference in macrocrack formation is clear, see fig. 25, 26 and 27, in which the cubes are 'unfolded' to show the complete crack pattern. Fig. 27 shows another example of localized shear bands at an inclination of about 20 degrees with the (principal) loading axis as found by Van Mier (Van Mier's planar mode fracture due to the presence of a preferential failure direction).

ri ht back bottom

Figure 26: Crack pattern for uniaxial test with teflon platen (Vonk)

\

)

Test T3-2

to

left front ri ht back bottom

Figure 27: Crack pattern for triaxial test with teflon platen (Vonk)

3.2.2. Multiaxial tests.

In the previous paragraph it Was seen that the pre-peak behaviour in uniaxial tests was hardly

influenced by the type of loading platen. Only an increase in peak stress and strain could be

research program by Gerstle et al. [344]. In this program six different loading platens were used by seven research institutes:

1. Dry steel platens (DP);

2. Steel platens with lubrication or anti-friction pads (LP); 3. Brush platens (BR);

4. Fluid cushions (FC); 5. Flexible platens (FP);

6. Standard triaxial test setup (CYL).

See figure 28 and 29. Biaxial and triaxial tests were carried out to obtain insight in the influence of the loading platens on the concrete behaviour. From fig. 30, 31 and 32 it is clear that also in triaxial tests the maximum bearable load increases with increasing boundary friction.

The only triaxial experiments known in which a comparison is made in the softening regime between several loading platens are those by Vonk [567], described in the previous paragraph. Though more researchers have carried out experiments to compare different loading platens (pre-peak), these will not be discussed any further because the results of Gerstle et al. give a good description of the phenomenon: loading platens introducing large shear stresses should not be used in experiments because:

1. Peak stress increases with increasing boundary shear;

2. Concrete behaviour seems to become more ductile with increasing boundary shear. For an excellent overview of loading platens used in the past (-1985) see Winkler [492].

(•

IP.

~~

'~EJ~~

~RIGID

STEEL

T

~ATENS

Ory Steel Plates fr;;>J

Flu ld CuahlOft (FC)

LUBRICATION OR:

ANTI FRICTION PAOSj p •

~

Y.• . P,

'

i I .!llil:illllllllll

P~:[]:~X

.

u

_P,

~

EJ·.

~

X,u 1 w:u0 c ·- ~ ~ u2uo

if

·

-I I ' ~

=

=

-I I =

=

- ---~\\1

i

"\.

RIGID STEEL ~ATENS ~trel l"latf.•j w11h Lul.trH·ation

1111111111111111

BRUSH ~PLATENS

or .~ntL-triCt\on Pads 'LP> ~rUSI\ ~·arm&: Plltf'n?i -1.BRJ

uftr

~~Gt·~-IT"ITT

STEEL PISTONS

~ fLASTOMERIC PADS

lllOIDITY:co lllOIDITY:O • on

..

•

.

0

..

,,.

o• o•

·-

..

..

-~

...

_•• c .. 0 ... -c ""''

..

· - ooj!Ct

..

..

.

·-

-~ •::;

FlllCTION:O FRICTION :oo

Figure 29: Classification of loading platens used by Gerstle et al. [344]

• &-:•-1 ·~~1

..

1 - '

J

_I

:

!--r-'.,:. _~~, • . _. I • I -I I . ~IN Ill

.

_l•l (<) ·I _{·• ·IC""l} (6) .J, ., ·• ·~ •I _·•l'-l l•l

..

( ... ,,..,) I

,.,

COloC,.lt[SSION ., ·• ., c··~ I, (Mfillrn1

--v~r!,

--1!!'·~·o~·~~....L~..L~...L£!!!:2'.!!J~lll!L..L I -l _{-· [•t.J} (cl (di

1.4 -v

-

1. 2 ... - ..lC

-1.0

_i

/

--0.8

FC

FP

BR

LP

DP

Figure 31: Compressive strength as a function of the type of loading platens (Gerstle et al., after Van Mier [399))

. . . • •O" • • ... .. -, ,. C!J 1•tL • .,,. • I MIL -l.,. D ORIENTATION SKllCH -TUM - · ·

e

11•tU -O' t .... u -&. ,. 0 cu -· c ~ PATH 3

Figure 32: Triaxi.alfailure envelope using different loading platens by Gerstle et al. [344]

From recent research by Vonk [606] it can be concluded that for both uniaxial and triaxial tests brush platens give the most satisfying results up to peak stress, beyond peak teflon platens appear to perform better.

3.3. Nonuniformity of deformations

Vonk [606] investigated the effects of nonunifonn loading both experimentally and numerically. To set up a numerical model Vonk developed an analytical model, shown in fig. 33, which includes the parameters influencing rotation of the loading platen. Nonunifonn loading in compression tests are caused by eccentricity of the load, nonparallelism of loading platen-specimen surface and nonflatness of this surface. The latter was not included in Vonk's model.

F

a

h

w

Figure 33: Analytical model of a uniaxial compression test (Vonk [606))

The model, leading to a stability criterion similar to the one by Hassanzadeh [ 517], showed that rotation <p of the loading platen inc~eases when:

- the eccenctricity e and the initial rotation <po increase ( <p depends on the accuracy of testing); - the rotational stiffness of the loading apparatus C;

- the cross section bxd of the specimen increases ( <p is quite sensitive to this change in cross section);

- the combination of stress cr and dcr/dw (w is the averiage deformation of the specimen) becomes more critical. This means:

- more brittle types of concrete; - specimens of greater height

The model proved to give a good description of the behaviour observed in the tests, carried out by Vonk (see previous chapter). Softening stimulates non-unifonnity of deformations, that can have a significant influence on the stress-strain curve. Vonk stated: "Like localization of deformations, the stimulation of nonuniform deformations belongs to the structural behaviour of a softening test It can be looked upon as another example of softening to localize in the smallest volume possible."

Hinged loading platens appeared to be very sensitive to an eccenctricity of the load, fixed loading platens to an initial angle between loading platen and specimen surface. As said before, hinged loading platens show large rotations when softening occurs, stimulating nonuniform defonnations.

In fig. 34 the influence of nonunif onn loading in simulations with Vonk' s model is shown

(compared with a uniaxial experiment by Vonk). In multiaxial experiments rotations of the

loaded boundaries will not occur, because the specimen is enclosed by the loading platens in

multiple directions. -•O

I

-30 m ; -10 O'----'---'---L...-~-~ ~ -~ -~ -M -~ -W Naninat deformation lm-nJ -50 r---~ - Cak:ula1ion -0.2 -0.4 -0.6 _-o.e 0.fom'ation lnYn)

I

-30 -40 -10 - f/J₀=0.000 - - - ep₀=0.001 - - IP ₀=0.002 · • · • · ct>0=0.003 · - ep0=0.004 o~--~---'----'---'----l 0.0 - 0.2 - 0.4 - 0.6 - 0.8 - 1.0 Nominal deformation [,,...,...] :I 5 ~

..

_..

> ~ iii a: 0.95 0.90 0.85 0.80 ~---~---' 0.000 0.00' 0.002 0.003 0.004

Initial rotatiori [rad!

Figure 34: Left: Influence of nonuniformity of deformations on the stress-deformation relation of a uniaxial test. Right: Influence of an initial angle between specimen surface and

loadin$ platen (Vonk [606])

It can be concluded that the effects, introduced by the test environment, discussed in this chapter can not be neglected when performing compressive (softening) tests on concrete.

Though it is difficult to quantify the influence of loading apparatus stiffness and layout (and in

most cases of the loading platens used), it is necessary to take all test environment

characteristics in account when simulating concrete behaviour or when comparing test results from different laboratories.

3.4. Keywords for chapter 3.

-Boundary conditions I Loading platens.

4. Influence of stress path

4.1. Proportional versus non-proportional stress paths.

In most multi.axial experiments loading is applied through proportional load paths, i.e. constant

ratios of cri/crJa3 or wi/wJw3• In practice however the occurrence of other load paths is very

likely. Therefore several researchers examined the influence of the loading path. In 1972

Kobayashi and Koyanagi carried out biaxial tests on lightweight concrete specimens, in which proportional, sequential ('stairway') and 'random' stress paths were followed [260], figure 35, and concluded that no significant influence on the biaxial failure surface occurred due to differences in stress path. These findings were confirmed by tests by Nelissen [263].

a,;fk

1

1.5 ~----.--·...--.---,,.----r---;( 0.5 • prop. load. o seq. loa 0 10) 2ro 300 400 0 0.5 1.0 1.5 Pz [ kN] 02/fk

Figure 35: Biaxial stress paths investigated by Kobayashi/Koyanagi (after Van Mier [399])

Taylor and Patel [305] tested normalweight concrete with three different strengths under both proportional and sequential biaxial stress paths and found that the ultimate load was slightly larger for specimens loaded through sequential paths. Recently (1993), Torrenti et al. carried out biaxial experiments on both mortar and normalweight concrete following proportional and sequential stress paths [612]. Two types of load application systems were used. A small influence on the strain levels at failure was observed, though the difference between the two

applied loading systems appeared to be a factor of major influen~.

In triaxial tests the influence of stress paths has been investigated in the cooperative research program in the late 1970's by Gerstle et al. [344], mentioned in the previous chapter. Four. different stress paths were examined, figure 36. The stress-deformation relations within the

deviatoric plane were found to be inde~ndent of stress path variations. Of course the shape of

"• - ~ (-, ' "2 ' •,)

o-tci

<r~

rrkr

~o-

er,

a;, --

~

--

~=.:

-- -

er.

~ . ~

• a::

TIME TIM TIME

'"'"' PATH I PAlH i PATH 4

c.a;>o c.a;>o llapo ll~)6fT~

ll<r,~ c.a;=. t.aozC>ai IOHU TUii AND

= 11J.D.ai L:laj•-60; Cl a; =-2llaj _{10111 UMI}

Figure 36: Stress paths in the test program of Gerstle et al. [344]

In 1979 Kotsovos carried out triaxial tests on cylindrical specimens following the stress paths

shown in figure 37 [361]. He concluded that no stress path dependency occurred up to a

hydrostatic stress of approximately 0.8 times the uniaxial compressive strength. The observed

path dependency beyond this limit was contributed to microcracking under hydrostatic

loading. - - Patti l • · ~ c ~

Figure 37: Stress paths examined by Kotsovos [361]

experiments by Stankowski [474]. In Stankowski's triaxial tests (non-proportional stress paths) the emphasis was laid upon the coupling between hydrostatic and deviatoric material responses. In 1989 Smith et al. found, by carrying out triaxial tests on cylindrical specimens, that the transition from volume compaction to dilatation (zero volume change) was found to be stress path independent and always at approximately the same distance from the failure envelope [564].

Specimens in the biaxial and triaxial tests carried out by Van Mier (see previous chapters) were loaded according different constant stress-ratio or constant displacement-ratio paths (proportional paths). See figure 38.

lil1.01 (compression)

o.'\

~

Is Is

:!. c3

I.~

.

I~

~\

/9

;cf/

\ i

I \ J /

\

.

/I

\

I tension) (com~ession)

Figure 38: Stress- and deformation paths in Van Mier's triaxial tests [466]

The stress-strain curves for the displacement-ratio curves showed, both in the biaxial compression and the tension-compression region, two successive peaks. A first one in the major principal direction, the second in the intennediate (in tenns of displacement) principal direction. This is in fact a result of a rotation of the loading against the specimen's 'damage

axes' and the direction of fracture planes caused by the first loading, see fig. 39. Such

'rotation-tests' will be discussed in chapter 4.3.

While in stress-ratio experiments a peak stress in the three loading directions is observed at the same time, the response of a defonnation-ratio test is largely dependent of the defonnational properties of the concrete. The scatter in (strength) results appeared to be larger for the displacement-ratio tests and for tests with higher minor principle (compressive) stress.

Other aspects of different loading paths in Van Mier's tests were already discussed in chapter 2.2.

As mentioned in chapter 2.2. Smith et al. [564] applied two different load paths in their tests .. In fig. 40 all test results are presented in terms of a 'zero volume change envelope' in the rendulic stress plane. From these results it was stated that "the onset of zero volume change appears load-path independent". Besides these tests, some 'wedge experiments' were carried out, which were especially interesting with regard to constitutive modelling.

u·₁1u2 = -1.0/-0.33 03 =O 0,-1..1 -160

i

-140 ~ =: -120 0 ~ ::; -'00 ~ -80 10 LS 2D l.S ID .S - - - Imm) u3 u casting-surface 02·"2 o1.u1 ~•Tl.ll'Y macro-cracks (fa~ure in 1-l plane! .5 1.0 tS 2.D 2.S 3.0 u₁1 m m J -- -70 E ~ z 0 -60 ~ -so ·40 -30 -20 -'O 0 0

c7

:::i Ci. o~ o1.p = 60.9 N/mm 2 I

I

I

I

/, I

I.

Ii

/ / Ii _/

Ii

/ oz.p= 34.0 N/mm2 " / Ii . · / -lJ -20 -1) -40 _-so

Figure 39: Biaxial constant displacement-ratio test (Van Mier [466])

-25 -20 ~ en _-15 e'. (T') I

....

_x -10 <!I ... en -5 0 0 -2 MAXIMUM STRENGTH CTC

+ EPSVPEO ALL CTC TESTS

*

EPSVP=O MULTISTAGE

-4 -6 -8

SIGMA-1

*

SQRT2 (KSI]

-10 -12

Figure 40: Peak strength and zero volume change envelope for different stress paths

(Smith [564])

4.2. Damage from previous loadings

4.2.1. Cyclic loading

Many researchers have carried out experiments on the behaviour of concrete under cyclic

In 1964 Sinha et al. examined the behaviour of concrete under uniaxial cyclic compressive loading [115]. In figure 41 a typical stress-strain curve is shown for this kind of test, showing loading- and unloading-branches. It was concluded that the 'envelope curve' (the curve joining the end points of the loading curves and the start points of the unloading curves) was unique for one type of concrete.

0 ool ool.

Figure 41: Cyclic stress-strain behaviour in uniaxial compression (Sinha et al.[ 115])

Spooner and Dougill [314] carried out cyclic experiments on 250x75x75 mm concrete prisms at a strain rate of 0.002/min. After every loading the specimens were unloaded completely. Some test results are plotted in fig. 42. ·

"

IO

·o

Ca••••tl•" '""._....,..•MO-•

-•t'Ol'f ... COOOIUl ... \1Jtli1~

~tJ.<rWt•cr•""" 1000 Pl.AIM• I~ 10 1000 '''" '"'

Figure 42:Cyclic uniaxial stress-strain results (Spooner)

The most important findings of Spooner and Dougill were the following:

"" HOO

1. With increasing maximum strain the initial slope of a reloading stress-strain curve decreases; 2. With increasing maximum strain the reduction of length of the specimen after unloading increases, indicating an increasing irreversible damage;

3. During the first loading the stress-strain curve is curved, whereas it is much more linear during the second loading;