  This paper describes a KGD-type model of a hydraulic fracture created by
injecting fluid in weak, poorly consolidated rocks. The model is based on the
key assumption that the hydraulic fracture is propagating within a domain where
the hydraulic fields are quasi-stationary. By further assuming a negligible
toughness, the fracture is shown to grow as a square root of time. The
asymptotic fracture propagation regimes at small and large time are constructed
and the transient solution is computed by solving a nonlinear system of
algebraic equations formulated in terms of the fracture aperture. At early time
the fracture is hydraulically invisible and the injection pressure increases
with time $t$ as $\log t$, while at late time leak-off from the borehole is
negligible and the injection pressure decreases as $t^{-1/4}$. According to
this model, the peak injection pressure observed when injecting fluid in weak,
poorly consolidated rocks should not be interpreted as indicating a breakdown
of the formation, but rather as marking the transition between two asymptotic
flow regimes. The timescale that legislates the transition between the small
and large time asymptotic regimes is shown to be a strongly nonlinear function
of a dimensionless injection rate.
