  We have calculated the evolution of cosmic ray (CR) modified astrophysical
shocks for a wide range of shock Mach numbers and shock speeds through
numerical simulations of diffusive shock acceleration (DSA) in 1D quasi-
parallel plane shocks. The simulations include thermal leakage injection of
seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion
is assumed. We model shocks similar to those expected around cosmic structure
pancakes as well as other accretion shocks driven by flows with upstream gas
temperatures in the range $T_0=10^4-10^{7.6}$K and shock Mach numbers spanning
$M_s=2.4-133$. We show that CR modified shocks evolve to time-asymptotic states
by the time injected particles are accelerated to moderately relativistic
energies ($p/mc \gsim 1$), and that two shocks with the same Mach number, but
with different shock speeds, evolve qualitatively similarly when the results
are presented in terms of a characteristic diffusion length and diffusion time.
For these models the time asymptotic value for the CR acceleration efficiency
is controlled mainly by shock Mach number. The modeled high Mach number shocks
all evolve towards efficiencies $\sim 50$%, regardless of the upstream CR
pressure. On the other hand, the upstream CR pressure increases the overall CR
energy in moderate strength shocks ($M_s \sim {\rm a few}$). (abridged)
