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Unstable rock is a kind of global geological disaster with high frequency. This paper, considering three kinds of combined loads which are gravity, fracture water pressure and seismic force, constructs a unstable rock mechanics model and it uses a fracture mechanics method to deduce the composite stress intensity factor of the type I - II. Based on the maximum circumferential stress theory, this a rticle calculates the theo-retical fracture angle by triangle universal formula.

Rock is a complex structure which is naturally produced by one or more minerals under geological conditions. In the rock engineer, most rocks belong to pressure-shear condition. Therefore, it is necessary and urgent for the study of unstable rock in pressure-shear condition. A lot of scholars have devoted themselves to the study of unstable rock. For example, Nara Y. etc. [

_{L} is horizontal seismic force per unit length; P_{V} is vertical seismic force per unit length; W is Gravity of rock mass per unit length.

In

In the straight line of the unit which parallel to the

It will find

A new and old coordinate system is established in

It can know

Combining formula (2), formula (3), formula (4) and formula (5) can be obtained

By formula (6) can be known

The article assumes

Because of

We can carry out partial differential to Westergaard stress function

From formula (13), formula (14) and formula (15), we can get

As shown in

The stress function is obtained

The original O point translates to the new coordinate O' point. We assume complex coordinates of any new coordinates of a bit is

Combining formula (16) and formula (17)

When

Because of

Combining formula (18), formula (19) and formula (20), we can obtain

We can use the same way to get

At first, we suppose that composite stress intensity factor is

Because the horizontal seismic force (P_{L}) and vertical seismic force (P_{V}) can not be considered at the same time. So we can add a coefficient C_{1} and C_{2} in front of them respectively. It builds the following functions

where the coordinates of the center of gravity of the unstable rock is_{0}; Sum of forces in the axial direction of

If D_{1} and D_{2} are constants, according to Westergaard’s stress function, we will get

Combining formula (7), formula (21), formula (22), formula (23), formula (27), we will calculate

According to the maximum circumferential stress theory [

We put trigonometric function into formula (29), and it will get

When it is negative (“−”), fracture angle is greater than 180˚. Obviously, it is not in conformity with the actual situation. So fracture angle is

Considering gravity, fracture water pressure and seismic force, this paper constructs unstable rock mechanics model, which is very common in the rock engineer. What’s more, we derive composite stress intensity factor of the type I - II by fracture mechanics. And according to the maximum circumferential stress, we calculate theory Fracture angle by trigonometric function. In short, the results have certain theoretical guiding significance and economic value for prevention of disaster and engineering safety assessment.

Chen, S.Q., Chen, H.K., Yang, M., Chen, T. and Guo, K.X. (2016) Analysis on Fracture Mechanics of Un- stable Rock. World Journal of Engineer- ing and Technology, 4, 69-75. http://dx.doi.org/10.4236/wjet.2016.43C009