**6. Conclusions**

terial, the fracture propagation is along the cracked bedding and form a straight fracture

~45o

is still along the tension failure bedding. With the increase of loading step, there is a high tensile stress area on the main fracture tip which is along the cracked bedding and the bed‐ dings in the high tensile stress area are cracked and form secondary fractures paralleling to the main fracture, moreover, with the increase of bedding angle, the number of secondary fractures is increasing gradually. Because of the advantage of main fracture, the fracture

tension failure bedding to the horizontal direction that is the main fracture and the secon‐ dary fractures paralleling to the main fracture is still initiating and propagating in bedding plane with the horizontal secondary fracture initiating at the same time and connecting the main fracture and the parallel secondary fractures gradually. In this case, the bedding plane

along the bedding plane. Because of the heterogeneous characteristics of rock and bedding materials, different strength elements are in random distribution causing an uneven stress distribution and the local stress concentration thus making the fracture become bend and rough, but the general trend is the maximum principal stress direction. In this case, the ef‐ fect of bedding plane on fracture evolution is almost disappeared, but the maximum princi‐ pal stress controls the fracture initiation and propagation. Comparing figure 4 and figure 19, we can find that the existence of bedding influences the fracture shape greatly in the same

From the numerical simulation results, as bedding angle increase, the values of initiation pressure are 13.3MPa, 13.7MPa, 14.2MPa, 16.8MPa, 17.1MPa, 16.9MPa and 18.2MPa respec‐ tively, and the values of breakdown pressure 15.3MPa, 16.4MPa, 17.4MPa, 18MPa, 21.2MPa, 21.3MPa and 20.5MPa respectively. Both of the values of initiation and breakdown pressure are in a linear growth (figure 20) with the growth rate similar and as the bedding plane is

Because the fracture propagation is determined by the maximum principal stress and the bedding plane together when bedding angle is 60o seeing from the second group simulation,

stiffness of bedding material on fracture evolution will be studied under the combined ef‐

In the third group, the rock specimens with the same bedding angle but different materials are under the constant confining and increasing hydraulic pressure. As the strength of bed‐ ding material is constant (bedding strength/rock strength is 1), but the stiffness decreased

), the initiation and propagation of fracture

), the fracture will turn from along the

), the specimen is in

), the initiation and propagation of fracture is no longer

for example, in the third group, the effect of strength and

eventually. In this case, the bedding plane determines the fracture evolution.

and the maximum principal stress determine the fracture evolution together.

~90o

condition as the maximum principal stress controls the fracture evolution.

parallel to the maximum principal stress direction (bedding angle is 0o

fects of the maximum principal stress and the bedding plane.

When bedding angle α increases slightly (30o

508 Effective and Sustainable Hydraulic Fracturing

propagation is still along the main fracture bedding.

When the bedding angle α continues to increase (60o

When bedding angle α is big (75<sup>o</sup>

the most unstable situation.

taking the bedding angle of 60o

Based on the simulation results of three groups, the following can be concluded:

