Fracture mechanics model of a fault termination zone

A fault termination zone from Middle Eocene chalks near Beer Sheva, Israel, is analysed via a fracture mechanical technique. The zone consists of the end of the primary fault, three secondary faults and joints associated with these structures. We demonstrate that the shape of the first secondary fault can be obtained from theoretical fracture mechanical calculations. This shape also enables us to obtain the set of conditions which induced the observed structures. The technique reveals the relative importance of the different variables that appear in the theory. The most significant parameters in determining the shape of the first secondary fault are the vertical dimension of the primary fault, the ratio of the two horizontal differential stresses and the initiation angle of the secondary fault. Results indicate that the fault termination zone was created under an almost pure shear load. The true lateral displacement of the primary fault is unknown; hence, exact calculation of the stresses leading to the secondary fault is hardly possible. However, an estimation, based on a partial conversion of this displacement to an uplift, yields σ1 and σ3 values at initiation of between 3.8 and 7.6 MPa and 3.65 and 7.3 MPa, respectively.