Drained joints, undrained matrix, intermediate time

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

e &=& - a_11p_c - a_12p_f^(1) -^(2) &=& -a_31p_c - a_32 p_f^(1),   showing that the pore-pressure buildup in the matrix is

B[u^(1)] . p_f^(1)p_c |_^(1)=p_f^(2)=0 = - a_21a_22.   Similarly, the effective undrained modulus for the matrix phase is found from (dcum) to be determined by

1K[u^(1)] - . ep_c |_^(1)=p_f^(2)=0 = a_11 + a_12B[u^(1)].  

Notice that if a₂₃ = 0 then (EB3) and (B1) are the same.