CHARACTERIZATION OF CONCRETE IN MIXED MODE FRACTURE UNDER
CONFINED CONDITIONS
1
O. I. Montenegro1, D. Sfer2, I. Carol1
ETSECCPB (School of Civil Engineering)-UPC (Technical Univ. of Catalonia).
Jordi Girona 1-3, Campus Nord, Edif D-2.
E-08034 Barcelona, Spain.
Email: [email protected], [email protected]
2
Universidad Nacional de Tucuman – Instituto de Estructuras.
Avenida Roca 1800.
4000 – Tucuman – Argentina.
Email: [email protected]
ABSTRACT
In spite of significant research efforts devoted to concrete fracture in the recent past, fracture of this material under confined
conditions remains largely unstudied. Some models have been proposed which advocate for an asymptotic mixed mode or
"mode IIa" with a second fracture energy independent and significantly higher than the traditional mode I fracture energy.
Cracks under this mode IIa would be subjected to sufficiently high compression across the fracture plane, such that all
dilatancy would be suppressed and the crack would become sensibly straight cutting through aggregates and matrix. In this
paper, recent experimental work is described. The specimens employed are similar to those proposed by Luong [1,2], and
consist of short cylinders with coaxial cylindrical notches on top and bottom faces leaving an also cylindrical ligament. They are
loaded vertically on the outer (top face) and inner (bottom face) rings, originally with no confinement. In the setup developed,
this specimen is introduced in a large-capacity triaxial cell, protected with membranes and subject to different levels of
confining pressure prior to vertical loading. Measurements include vertical as well as circumferential displacements. Results
agree well with expected trends of mode IIa, and indicate that this may be a useful technique to evaluate the corresponding
fracture energy.
Introduction
I
The classical mode I fracture energy, Gf , is a parameter frequently incorporated in many concrete models. Some models also
consider a second fracture energy in mixed mode; however, a generally accepted criterion does not exist yet for this type of
fracture in concrete, especially under confined conditions, which on the other hand may be relevant in many engineering
problems such as highly reinforced columns, impact, explosion, etc.
In the 90s, the Group of Mechanics of Materials of the School of Civil Engineering at UPC Barcelona (ETSECCPB-UPC),
introduced the concept of asymptotic shear-compression mixed mode or mode IIa, consisting of a shear state with very high
compression level across the fracture plane, such that all dilatancy would be suppressed and the crack would become sensibly
straight, cutting through aggregates and matrix [3,4,5].
In conventional concrete, the strength of the aggregates is larger than that of the mortar, and the interface between them
represents the weakest part of the composite. Thus, in mode I, the cracks are normally initiated in the aggregate-mortar
interface and then are connect each other through the mortar, giving rise to the winding trajectory of Fig. 1a. On the other
hand, mode IIa consisting of a shear displacement with a totally suppressed dilatancy and a straight crack cutting trough
aggregates and mortar, is depicted in Fig. 1b.
(a) Crack in mode I.
(b) Crack in mode IIa
Figure 1. Crack paths.(a) Crack in mode I.(b) Crack in mode IIa.
In this paper, results are presented concerning the experimental study to generate cracks in shear-compression, with the final
objective of verifying the existence of mode IIa, and calibrating the corresponding parameters, mainly the fracture energy GfIIa.
To produce a crack in shear-compression along a pre-established plane or surface, and to control independently the normal
and shear stress acting on it are non-trivial tasks. Previous efforts along this line include the shear-compression cube test [6],
in which is not possible to control the level of compression independently of the shear load, the shear compression test of
Swartz and Taha [7] which consist of notched beams subject to transversal compression, although the results show that there
were many cracks in different planes. Finally there is the “punch through shear test” in rock [8] which uses cylindrical samples
with circular notches drilled from the top and bottom faces, subjected to different levels of pressure confinement, similar to the
ones proposed in the present study.
In the present study, a new test setup has been developed based on the original proposal by Luong [1,2], that consists of short
cylinders with coaxial cylindrical notches on top and bottom faces leaving an also cylindrical ligament. In the new setup, similar
specimens are introduced in a large-capacity triaxial cell, protected with membranes and subjected to different levels of
confining pressure prior to vertical loading.
Specimen Geometry
The cylindrical specimens have a diameter of 100 mm and a height of 40mm, with coaxial cylindrical notches of 10mm depth
on both top and bottom faces which leave an also cylindrical shear fracture ligament of 20mm height. Specimens are cast in
moulds of 100 mm diameter and 200mm height. Cylinders are then cut with a diamond saw and they are surface ground with a
diamond disc to obtain the 40mm high specimens. Finally, notches are produced with drills similar to those used in core
extraction.
The top and bottom drills have slightly different diameters, so that, given their finite thickness, the fracture surface going from
outer side of top notch to inner side of bottom notch, remains as vertical as possible. A diagram of the specimen and
diametrical cross section are shown in Figs. 2 and 3.
47
23,5
21
52
21
40
23,5
100
Fig. 2. View of specimen.
Fig.3. Cross-section of the specimen (units in mm).
Loading System
In Fig. 4a, the specimen and load platens are represented. Two types of tests need to be distinguished: the unconfined test
(Fig. 4.b), and the confined test (Fig. 4.c). The lateral confinement pressure is obtained by introducing the specimen and
platens in the triaxial cell, as seen in Figure 5.a.
(a)
(b)
(c)
Fig. 4. (a) Load system. (b) Load state in unconfined test. (c) Load state in confined test.
The loading platens were designed to carry out both the confined and unconfined shear test. As shown in Figure 4.a, the
upper platen sits on the outer part of the specimen, while the lower loading platen supports the specimen under the central
part of it. Additionally, an outer steel cylinder seats under the specimen in order to provide continuity to the outer surface of the
entire column of specimen + loading platens, which is a requirement in the confined tests. This outer lower platen is in turn
sitting on a set of springs, which provide some compression component on the outer-lower specimen-platen contact (important
for avoiding problems with the membrane), and also provides stability to the system for better control of the post-peak branch.
The confined test arrangement is shown in Fig.5a. The WIKEHAM/FARRANCE cell was originally designed for 15x30cm
cylindrical specimens and 140 MPa of maximum confining pressure [9]. In this case, the specimens are only 10cm diameter
(coinciding with the piston diameter), which leaves ample room for the measuring equipment. The difference in length is
covered with the specially designed loading platens, hinge device, etc. Specimen and hinge device are protected with
membranes to isolate them from the confining fluid, avoiding the penetration of pressure in the contact specimen-load platens,
which would generate undesirable vertical loads and disrupt the test. In this way, lateral pressure may be applied
independently of vertical load on the specimen.
Two special loading platens have been designed to avoid the penetration of the oil along the horizontal contacts, the upper
platen which incorporates two types of seals (o-ring and trapezoidal seal) and the lower platen which incorporates a linear rod
seal (PTFE fluid power seal) allowing the vertical movement of the cylindrical platen without oil intrusion, see Fig. 5b, and 5c.
For the confined tests, the lateral confinement pressure is applied first and remains constant during the entire duration of the
test. Confined tests are repeated for different levels of lateral confinement pressure in order to identify and calibrate the
fracture energy for the asymptotic mode IIa, which should be achieved for a sufficiently high confinement pressure.
(b)
(c)
(a)
Figure 5. (a) General diagram of confined shear tests, (b) and (c) especial seals in loading system.
Materials
The characteristics of the concrete materials used to cast the specimens are summarized in Table 1. All tests have been
carried out on specimens that are older than 28 days.
Material
Conventional
Concrete
High Strength
Concrete
Mortar
Max. Size
of
aggregate
[mm]
f c' [MPa]
E [MPa]
8
56
25000
10
90
35000
-
56
25000
Table 1. Materials.
Measurement Devices
LVDTs connected to the loading platens are used to measure the vertical displacements which in turn give rise to the shear
displacement produced in the fracture plane. Submersible LVDTs capable of operating under up to 21 MPa fluid pressure are
used to measure the vertical displacement inside the triaxial load cell. A circumferential chain equipped with a clip
extensometer is used to measure the specimen’s circumferential displacements. This device has been also designed to
operate suitably inside the triaxial load cell. The confinement pressure has also been measured by using a pressure
transducer placed in the triaxial cell.
In Fig. 6, the specimen together with the submersible LVDTs can be seen before the whole specimen+platens system is
introduced in the cell.
(a)
(b)
Figure 6. (a) Image of specimen for confined test before being introduced in the triaxial cell. (b) LVDTs connected to load
platens.
Results
In order to verify the test setup, a first experimental test series has been carried out, which includes unconfined and confined
shear tests. The tests inside the pressure cell were carried out at two different levels of confining pressure (2 and 4MPa).
Unfortunately, due to a problem with the measuring devices, only the data for tests at 0 and 2 Mpa confinement is available.
The available test results are represented in terms of shear stress vs. vertical displacement and vertical vs. circumferential
displacement curves (Figs. 7 for unconfined tests and 9 for confined tests). Images of the specimens after testing, showing
cracks, etc. are also shown in Figs 8, 10 and 11.
30
High strength
concrete
0.2
Vertical displacement [mm]
Shear stress [MPa]
Mortar
-0.4
0
0.4
0.8
1.2
20
Radial displacement [mm]
0
10
Conventional
concrete
Mortar
-0.2
-0.4
Conventional
concrete
0
-0.4
0
0.4
Displacement [mm]
(a)
0.8
1.2
High strength
concrete
-0.6
(b)
Figure 7. (a) Shear stress–vertical displacement curves, (b) radial displacement–vertical displacement, in unconfined shear
tests of three different materials.
Fig. 7.a shows the shear stress–vertical displacement curves, and Fig. 9.b their corresponding dilatancy curves. In all cases,
after the peak one can observe a steep descending branch, changing later to a more gentle slope. This may be associated to
the transition between two different mechanisms: first the cracking of the cylindrical ligament between the notches occurs
under shear, which is then followed by the opening of four to five tensile radial cracks. These cracks are produced due to the
dilatancy generated on the original cylindrical crack as the external ring starts sliding with respect to the central cylinder. Once
the tensile radial cracks have opened, the shear stress transmitted across the ligament tends to vanish. Fig. 8 depicts the
tensile radial cracks produced in a specimen without confinement.
Figure 8. Picture of tested specimen, unconfined shear test.
In Fig. 9, the shear stress–vertical displacement and radial displacement–vertical displacement curves for the tests at 2MPa
lateral confinement pressure are represented, together with the curves of the previous unconfined test, both for the
conventional concrete with max. aggregate size tmax=10mm.
40
0.1
2 MPa
0
Radial displacement [mm]
Shear stress [MPa]
30
20
-1
0
1
2
3
4
-0.1
2 MPa
-0.2
-0.3
10
-0.4
0 MPa
0 MPa
0
-1
-0.5
0
1
2
Displacement [mm]
(a)
3
4
Vertical displacement [mm]
(b)
Figure 9. (a) Shear stress–vertical displacement curves. (b) Radial displacement–vertical displacement in unconfined and
confined (to 2MPa) tests.
Note the higher peak load and asymptotic tendency to a residual non-zero value in the shear diagram, while dilatancy is very
much reduced as could be expected according to the mode IIa definition.
From the viewpoint of post-mortem specimen observation, tensile radial cracks were observed even up to 4 MPa of lateral
confining pressure in a conventional concrete with 10mm of maximum aggregate size (tmax), as shown in Fig. 10.
Figure 10. Photograph of tested specimen in confined shear test to 4 MPa of confinement pressure.
Existence of mode IIa (asymptotic mode)
The existence of a trend towards the predicted mode IIa of fracture may be observed in the previous results, since dilatancy is
clearly reduced with confinement and at the same time the area under the shear curve, associated to energy dissipation is
increased (Fig. 9).
With respect to the crack becoming straight and cutting through aggregates and mortar, this type of crack tendency was
verified in a preliminary series of confined shear tests without measurement of the vertical or circumferential displacements
inside the triaxial cell. Fig. 11 shows a photograph of a specimen tested under a confining pressure sensibly higher than 4
MPa, in which it can be clearly seen that the fracture plane follows an approximately straight vertical line, cutting through the
microstructure. The specimen does not show any observable radial cracks either, clear indication that dilatancy was very much
reduced or eliminated altogether.
Figure 11. Fracture surface in specimen tested at high confinement
Concluding remarks
From the experimental results presented in this paper, the following preliminary conclusions may be drawn:
ƒ
The proposed test arrangement seems to be capable of producing a controlled crack under shear-compression
which, for higher confinement pressures, will lead to the expected “mode IIa” of fracture. The results obtained agree
well in qualitative terms with the predictions of the parallel numerical calculations.
ƒ
The unconfined shear tests show that high-strength concrete has a more brittle behaviour than normal strength
concrete, and in turn that its shear strength is also higher. In the same tests, mortar exhibits a more brittle behaviour
in the softening branch than conventional concrete.
ƒ
Shear strength and ductility are substantially increased with lateral confinement.
ƒ
Tensile radial cracks are still present for lateral confining pressures of 2 MPa, in a conventional concrete with tmax=
10mm, On the other hand, dilatancy effect is significantly reduced for higher lateral confining pressures.
The work reported is part of an on-going research to characterize mixed-mode fracture under confinement. Current efforts are
aimed at new series of tests with increasing lateral pressure in which all measurements may be obtained. Also, the procedure
to evaluate quantitatively the GfIIa fracture energy from the experimental results has been preliminarily developed and is being
verified. This procedure involves also the classical Mode I energy, which requires additional experimental tests to be
evaluated. The research plan also includes numerical simulations including zero-thickness interface elements along all fracture
paths, for better interpretation/backanalysis of the lab tests, as described elsewhere [11].
Acknowledgments
The work presented has been mainly financed by projects MAT2003-02481 and BIA2006-12717 funded by MEC (Madrid). The
first author is grateful for the doctoral fellowship FPU-MEC. The second author had an MEC mobility research fellowship (for
young doctors) from 2004-2005 and in February of 2006 visited UPC financed by grant 2005SGR-L-00291 from Generalitat de
Catalunya (Barcelona).
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nd
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