There are several different, but equally valid, choices of time scale on which to define Skempton-like coefficients for the matrix/fracture system under consideration. Elsworth and Bai  use a definition based on the idea that for very short time both fluid systems will independently act undrained after the addition of a sudden change of confining pressure. This idea implies that which, when substituted into (generalstrainstress), gives
-e = a_11p_c + a_12p_f^(1) + a_13p_f^(2) 0 = a_12p_c + a_22p_f^(1) + a_23p_f^(2) 0 = a_13p_c + a_23p_f^(1) + a_33p_f^(2). Defining
B_EB^(1) . p_f^(1)p_c|_ ^(1) = ^(2) = 0 and B_EB^(2) . p_f^(2)p_c|_ ^(1) = ^(2) = 0 we can solve (EB1) for the two Skempton's coefficients and find the results
B_EB^(1) = a_23a_13-a_12a_33a_22a_33-a_23^2 and
B_EB^(2) = a_23a_12-a_13a_22a_22a_33-a_23^2. The effective undrained modulus is found to be given by
1K_u^EB - ep_c|_^(1)= ^(2)=0 = a_11 + a_12B_EB^(1) + a_13B_EB^(2).
These definitions will be compared to others.