Drained matrix, undrained joints, intermediate time

Next consider another sudden change of confining pressure on a jacketed sample, but this time the tubes are inserted in the matrix porosity so $\delta p_f^{(1)} = 0$, while $\delta\zeta^{(2)} = 0$. We will call this the drained matrix, undrained joint limit. The equations are

e &=& - a_11p_c - a_13p_f^(2) -^(1) &=& - a_21p_c - a_23p_f^(2)   0 &=& - a_31p_c - a_33p_f^(2),   showing that the pore-pressure buildup in the cracks is

B[u^(2)] . p_f^(2)p_c |_^(2)=p_f^(1)=0 = -a_31a_33.   Similarly, the effective undrained modulus for the joint phase is found

1K[u^(2)] - . ep_c |_^(2)=p_f^(1)=0 = a_11 + a_13B[u^(2)].   We may properly view Eqs.(B1), (Ku1), (B2), and (Ku2) as ``defining'' relations among these parameters.

Notice that if a₂₃ = 0 then (EB4) and (B2) are the same.