The end of this static loading corresponds to the beginning of creep
loading. Microcrack initiation generates a severe hygral imbalance
within the concrete. Local vacuums generated by cracks at the moment
of initiation generate local hygral shocks, resulting in water
concentration gradients and pressure gradients. These gradients induce
water vapor movement from capillaries bordering microcracks
towards these microcracks (Fick's law) and liquid water movement
(Darcy's law). These two types of movement lead to drying of the
capillaries concerned (reduction in the water meniscus). This selfdrying
induced by cracking causes additional shrinkage.
The microcracks created cross a large number of hydrates and
non-hydrated cement grains. Therefore, the microcracks constitute
access routes for liquid water and allow significant acceleration of
the kinetics of hydration of non-hydrated grains (phenomenon of
self-healing of microcracks). This mechanism increases the amplitude
and kinetics of self-drying shrinkage.
The fact that microcracking is considered responsible for basic
creep in concrete leads to the necessary existence of microcracking
kinetics (generating strain kinetics).
The density of microcracks generated during creep loading depends
on the propagation of microcracks created during static loading
(initial microcracks) and on the creation of new microcracks during
creep loading.
4.1. Microcrack initiation
When capillaries in the vicinity of initial microcracks in the concrete
are drained, self-drying shrinkage is induced around these
microcracks. The evolution of this self-drying shrinkage induces an
evolution of the stress field in the cement (the presence of grains
of sand generates tensile stress in the cement due its restrained
shrinkage). Consequently, local tensile stresses, which did not exist
at the end of the static loading, appear during creep loading. These
new local tensile stresses create new microcracks with kinetics
depending on the kinetics of capillary drying.
4.2. Microcrack propagation
Analysis of the propagation of initial microcracks is based on fracture
mechanics theory for pseudo-brittle materials, in particular
Barenblatt theory [16]. In Barenblatt theory, two systems of forces
exist at the crack front. The first is related to external loading (creep
loading here). This leads to concentration of the tension stress, the
intensity of which is reflected by the stress intensity factor K (which
depends on the external loading and crack length). The second system
involves cohesion forces (Fig. 14), which are attractive forces
between the particles on both sides of the plane of separation of the
crack (plane AB in Fig. 14) located in a very small zone of width
D bb L, where L is the crack length. For a given material, they depend
linearly on the spacing v of the lips of the crack, as indicated in Fig. 14,
and vanish when v reaches a certain limit (vm, Fig. 15). This second
system of forces also generates a stress concentration at the crack
end in opposition to the stresses generated by the external loading.
The intensity of this stress concentration is described by the stress
intensity factor k (which depends on D and v). When the crack does
not propagate, k exactly compensates K. The crack propagates when
k no longer compensates K, which occurs when the crack opening v
reaches a certain critical value. In the case of creep loading, the opening
of initial microcracks remains theoretically constant since the
mechanical loading is constant.
Conversely, as previously proposed, microcrack initiation during
static loading generates liquid water movements towards microcracks
recently created. The presence of water at a microcrack tip considerably
reduces cohesion forces (a well-known physical mechanism)
and thus the stress intensity factor k. This decrease in k leads to
microcrack propagation.
In summary, water transport in capillaries towards microcracks
is related to two physical phenomena: microcrack initiation and
microcrack propagation.