Drained test, long time

The long duration drained (or ``jacketed'') test for a double porosity system should reduce to the same results as in the single porosity limit. The conditions on the pore pressures are $\delta p_f^{(1)} = \delta p_f^{(2)} = 0$, and the total volume obeys $\delta e = - a_{11}\delta p_c$. It follows therefore that

a_11 1K,   where K is the overall drained bulk modulus of the system including the fractures.