The long duration undrained test for a double porosity system should also produce the same physical results as a single porosity system (assuming only that it makes sense at some appropriate larger scale to view the medium as homogeneous). The basic equations are

p_f^(1) &=& p_f^(2) = p_f, && ^(1) + ^(2) = 0, assuming the total mass of fluid is confined. Then, it follows that

e = - a_11p_c - (a_12+a_13)p_f, 0 = -(a_21+a_31)p_c - (a_22+a_23+a_32+a_33)p_f, showing that the overall pore-pressure buildup coefficient is given by

B . p_fp_c|_= 0 Similarly, the undrained bulk modulus is found to be given by

1K_u -. ep_c|_= 0 = a_11 + (a_12+a_13)B.

8/21/1998