3.2 Concrete
3.2.1 Concrete Uniaxial Compression Behaviour under Static Loading
Concrete is actually the most used construction material worldwide. It is not only eco-nomical; concrete also exhibits a usual high durability and is, by a correct manufacturing, deployable even in very adverse environmental conditions. As the principal components of concrete are hardened cement paste (as a result of the hydratation of water with cement) and concrete aggregates, it is expectable that these influence, among others, the mechanical properties of concrete. The water-cement-ratio plays for example a significant role in the compression strength development.
0.05 0.1 0.2 ε [%]
average
10 17 29 average
σ [MPa]
biaxial compression
tension
tension shear
(a) (b)
Figure 3.10:(a) Transmission of compression forces in concrete, redrawn from [44]; (b) Inter-face stresses between aggregate and cement paste, redrawn from [44]
Rogge [157] describes the stress distribution inside a concrete body. Accordingly, load stresses are transmitted mainly by the irregularly distributed aggregates. This leads to dif-ferent stress deflections, resulting in tension stresses between cement paste and aggregates which is a source of microcracks and cause for the initiation point of a microstructure weakening under compression as well as tension loads. Moreover, the aggregates are substantially stiffer and volume-stabler than the cement paste and obstruct its plastic shrinkage [16]. The interface between cement paste and aggregates is fundamental for the overall concrete strength. It represents the weakest link in concrete since the adherence strength has been proven to be lower than the cement tension strength. Among others, especially the aggregate type, its surface properties, the cement tension strength, and environment moisture are the principal parameters which govern the cement-aggregate
50 Chapter 3 Material Behaviour
adherence strength [44]. Following [44], the adherence strength is characterised by the components
• Mechanical adhesion (indentation) due to the aggregate roughness,
• adhesion owing to capillary forces,
• adhesion forces resulting from chemical reactions between cement and aggregates.
ε!₃ σ#₃
f! 0.8f!
0.4f!
F F
Crack growth in the cement paste, merging of microcracks Crack growth and additional crack formation in the interface between cement and aggregate Elastic behaviour (microcracks already present before any external loads are applied)
Figure 3.11:Phases of the stress-strain response under uniaxial compression (left), test speci-men short before failure (middle), and fracture pattern, redrawn from [124]
Under uniaxial stress states the resulting internal tension stresses increase with growing load stresses. After [57], concrete behaves linearly under unixial stress loading forσc3≤ 0.3fcwithc1=c2= −νc3and a Poisson’s ratio valueν=0.16. However, in [16] values are specified between ν = 0.15...0.25 for the concrete in the serviceability load range, whileν≈0.5 forσc3= fc, andν>0.5 forc3 >cu(volume dilatation). By stress values ofσc3 ≈0.4fc the microcracks, present at the interface between aggregates and cement paste and which already originate before any extern load is applied, begin to expand. By σc3≈0.8fcthey cross the cement paste phase, nearly parallel to the main load direction and the deformation behaviour becomes highly nonlinear [16]. The uniaxial concrete tension strength may be reached and the concrete element fails showing a high volume dilatancy c1+c2+c3≥0 [157], [57]. The specimen deformation does not concentrate on a single cross sectional area; it rather exhibits a fracture process zone where the concrete is split into individual lamellas which become unstable and begin to shear off whenσc3= fc[116].
The concrete presents afterwards – under a strain-controlled test – a softening behaviour which depends on the test facility configuration [178]. The fact that the concrete does not fails suddenly is due to the friction and indentation forces between the lamellas [116].
In the pre-peak spanc3≤cu, the compressive stress-strain constitutive equation may be approximated by a parabola with [92]
σc3=
(2c3+2c3cu)
2cu fc, (3.16)
3.2 Concrete 51
-σ"₃
-ε
"₃ -ε
"$
A"
f"
U"%
-ε
"₃
≈-(0.8...1.0)ε
"$
ε ε
"₁= "₂
ε ε ε
"₁+ "₂+ "₃= 0
ε ε νε
"₁= "₂=- "₃
(a) (b)
Figure 3.12:(a) Stress-strain response under uniaxial compression and influence of specimen length on strain-softening [92]; (b) Axial and lateral strains in a compression-tested cylinder [92]
wherecuis the concrete strain atσc3 = fc. For normal-strength concrete,cu≈2.0‰;
for high-strength concretes the values ofcumay increase [92].
By definition, the concrete Young’s modulus of elasticity may be defined either as the tangent inclination of the compressive stress-strain-curve (Ec0m) or as a secant inclination Ecmbetween the valuesσc3 =0 andσc3=0.4fc [16]. Ec0mas well as Ecmare determined by the stiffness of the aggregates and the cement paste. Also the water-cement-ratio and the hydration grade play a role [16]. Nevertheless, for normal-strength concrete, the aggregate stiffness may present the weightiest influence. Also the highest variability, since e.g. sandstone-based aggregates haveEagg=10000 MPa, while basalt-based aggregates may show values ofEagg=90000 MPa [16]; both are thereby stiffer than the cement paste.
On the other side, light-weight aggregates tend to be less stiffer than the cement paste.
Consequently, the Young’s modulus of elasticity is the result of an intricate interaction between cement paste and aggregates, moisture grade and concrete age; further the experienced load history, even if only in the elastic range, may affect Ec0m resp. Ecm decisively, see Ch.3.2.4.
In strain-controlled tests the concrete, subjected to uniaxial compression, exhibits a softening behaviour for values c3 > cu. It has been demonstrated, though, that this property reflects, in fact, rather the system performance; for instance, it is not an intrinsic material behaviour [175] and may be described using concepts of fracture mechanics.
Larger test specimens show e.g. a steeper decrease than short ones. The dissipated energy in the fracture process zone (the area as shown in Fig. 3.16) is strongly dependent on the specimen size and is further known as the specific fracture energyUcFper unit volume. Its value can only be derived from test results since a valid accepted mathematical model has not been found yet [92]. Nevertheless, due to the approximate size of the fracture process zone of twice the cylinder diameter, the values ofUcF oscillate betweenUcF = 60...160
52 Chapter 3 Material Behaviour
kJ/m3[175].
It has been observed that microcracks in concrete grow, even until failure, if the concrete is put under high constant uniaxial compression forces for a long time [154]. The creep strength is therefore defined as the compression strength which theoretically may be achieved, in this case from the concrete, infinitely long. Its value takes about 80% from the 28-day-compression-strength fc. Yet, the creep strength depends also highly on the point of time when compression loads are applied. The main reason may be found in the hydration process of concrete: By sufficient moisture the (young) concrete tends to continue hydrating – a process that increases its strength. Simultaneously, it also loses strength due to the mentioned microcracking.
It is worth mentioning that both uniaxial compression and tension strength generally decrease with increasing specimen size (size effect). According to [192], this phenomena expresses the higher probability of occurrence of material defects the bigger the specimen volume is. Further important factors are listed in [124].