The geosterss calculation model is able to reflect geosterss' physical nature and actual regularity. So far, a lot of scholars have established many geosterss calculation models, which include, Kinnick model [1], Mattews and Kelly model [2], Terzaghi model and Anderson model [3], Newberry model and Huang Rongzun model [4]. Although these models have considered the composition characteristics of geosterss in different aspects, the rocks were mostly treated as a homogeneous isotropic linear elastic material [5-7]. Due to the anisotropic characteristics of shale [8-11], there was lack of accuracy in the above mentioned models, and were no longer suitable for horizontal bedding shale [12, 13]. In addition, due to fragile shale core, the coring and the process of making specimen were difficult [14, 15]. The laboratory experiment (Viscous remanent magnetization, DSA) [16-20] and other experiment of geostress with core was more difficult. Therefore, it is necessary to carry on the research for the geosterss calculation model and retrieval method of horizontal beddings shale.

2. THE EXPERIMENT OF MECHANICAL PROPERTIES

The shale rock mass has good bedding structure, which leads to anisotropy of the mechanical properties of shale. The horizontal bedding shale of Liaohe Oilfield was selected as the research object. The bedding developmental state is shown in Fig. (1). The dry samples of shale were cored along the X`Y`Z directions selectively. All cylindrical specimens with the height to diameter ratio of 2 (±0.03) were prepared by cutting and polishing. The triaxial stress experiments were carried out with the machine of RAW2000. The full stress-strain curves and fracture morphologies were obtained. The results of Z1-1 are shown in Fig. (2).

Fig. (1). The horizontal bedding shale diagram.

Fig. (2). Full stress-strain curve and fracture of Z1-1.

According to the full stress-strain curves of each rock specimen, the elastic modulus, Poisson's ratio and compressive strength were calculated in X, Y, and Z directions. The results are shown in Table 1.

Table 1. The core elastic parameters in different directions.

	Core number	Elastic modulus /MPa	Poisson's ratio	Compressive strength /MPa
Along the Z	Z1-1	15280.6	0.27	137.34
	Z1-2	15448.4	0.25	132.53
	Z1-3	15097.8	0.26	128.97
Average	——	15275.6	0.260	132.947
Along the X	X2-1	9017.4	0.30	82.45
	X2-2	8487.8	0.31	84.86
	X2-3	8986.5	0.33	78.39
Average	——	8830.6	0.313	81.900
Along the Y	Y3-1	8743.2	0.34	79.21
	Y3-2	9086.4	0.32	90.32
	Y3-3	8424.3	0.29	86.54
Average	——	8751.3	0.317	85.357

The results showed that the values of elastic parameters that are parallel to the bedding plane (along the X and Y direction) were close, and which had large differences from the vertical to bedding plane (Z direction). The vertical values were significantly higher than the parallel values. The rock presents the feature of transversely isotropic.

The depth of the shale coring layer was 1600m. In the vertical direction to the bedding plane, the elastic modulus is 15097.8MPa and the Poisson's ratio is 0.32. In the direction of parallel to the bedding plane, the elastic modulus is 8790.9MPa and the Poisson's ratio is 0.36. In the adjacent homogeneous formations, the elastic modulus is 30927.3MPa and the Poisson's ratio is 0.22. The single factor was varied, the sensitivity factors and influence laws were determined simultaneously.

With the elastic modulus and Poisson's ratio of the vertical bedding direction increased, the in-stiu stress of two horizontal directions increased linearly as shown in Fig. (3a). With the increased Poisson's ratio, the geostress of two horizontal direction increased exponentially. The growth rate was higher for the maximum horizontal geostress. The difference between two horizontal geosterss increases gradually as shown in Fig. (3b).

Fig. (3). The sensitivities for the elastic parameters of the vertical bedding direction.

Fig. (4). The sensitivities for the elastic parameters of the parallel bedding direction.

With the increased elastic modulus of parallel vertical bedding direction, the in-situ stress of two horizontal directions was decreasing exponentially and the decrease rate of the minimum horizontal geostress was bigger, as shown in Fig. (4a). With the Poisson's ratio increased, the geostress of the two horizontal direction was increased linearly, the growth rate of two horizontal geostress is similar as shown in Fig. (4b).

With the increased elastic modulus of the adjacent homogeneous formations, the in-situ stress of two horizontal direction decreased exponentially. The decrease rate of maximum horizontal geostress was faster. The difference between the two horizontal geostress decreased gradually, and finally became equal, as shown in Fig. (5). The main reason was that, the adjacent formation had stronger ability to resist deformation and bear more tectonic stress.

Fig. (5). The sensitivities for the elastic parameters of the adjacent homogeneous formations.

When using the new method to predict the shale geostress by the adjacent homogeneous formation, the following procedures should be obeyed.

1. Combining with the indoor experiments or logging data, the shale elastic parameters of the vertical direction, parallel direction and the adjacent homogeneous formations should be calculated.
2. The geosterss of the adjacent homogeneous formations should be evaluated by the small scale fracturing or the laboratory experiment.
3. By appling the new calculation model, the geostress of the horizontal bedding shale can be obtained.

Based on the above procedures, the shale geostress of Liaohe Oilfield was calculated. Firstly, the sandstones adjacent with the shale were cored and the DSA experiment was carried out. The DSA experimental apparatus and rock specimens are shown in Fig. (6).

Fig. (6). The DSA test apparatus and specimen.

The vertical stress was 30.5 MPa. The maximum horizontal geostress was 36.2 MPa and the minimum horizontal geostress was 24.8 MPa. According to the geostress of the measuring point, the geostress of the shale layer was calculated by combining with Terzaghi model, Newberry model, Huang Rongzun model and the new model established in this paper. The results are shown in Fig. (7).

Fig. (7). The results calculated by different model.

Without considering the influence of tectonic stress, the calculation result of geostress by Terzaghi and Newberry model was lower. In the Huang Rongzun model, only considering the effect of Poisson's ratio, it was concluded that the maximum horizontal geostress value was larger and the minimum horizontal geostress value was smaller without the effect of elastic modulus. The new model considered the influence of Poisson's ratio and elastic modulus simultaneously. Thus, the calculation results were in the range of the results of Huang Rongzun model.

1. Considered the transversely isotropic characteristics, the new geostress calculation model and prediction method were established. The model and method were more convenient and precise for the horizontal bedding shale.
2. The sensitivity factors and influence laws were analyzed. The major influences of the shale geostress were the elastic parameters of its own and those of the adjacent bed. The accurate evaluation of the mechanical parameters of shale and adjacent layers provides a basis for calculating the shale geostress.