## 1 Introduction  
Shale oil and gas, as one of the important development directions in the energy field, have a huge resource potential that is becoming increasingly advantageous, and with the successful development of shale gas on a large scale, exploration research on shale oil is being actively conducted [1, 2, 3]. China is rich in shale oil resources [4, 5], and compared with the major shale-oil-producing basins in the United States [6, 7, 8, 9], China's terrestrial organic-rich shales have more complex geological characteristics, especially deep shale reservoirs, due to their unique depositional characteristics, resulting in extremely developed shale laminae, natural fractures, and other weak surfaces, which have an important influence on the hydraulic fracture extension behavior and eventual fracture geometry, which in turn affect reservoir transformation and the effect of reservoir modification [10; 11; 12; 13]. Therefore, it is important to study the influence of laminar surfaces on hydraulic fracture expansion for fracture modification in shale reservoirs.  
At present, scholars at home and abroad have conducted research on the interaction mechanism between laminar surfaces and hydraulic fractures. [PERSON] [14] carried out numerical simulations of stratified shale fracturing by StimPlan to study the differences in mechanical parameters explained by comparing the transverse isotropic model with the conventional model and the conversion of dynamic and static mechanical parameters of unconventional reservoirs, and studied the effect of the fracture initiation point on fracture morphology by changing the injection hole location. [PERSON] et al. [15] investigated the anisotropic dynamic-static properties of shale by conducting a proposed triaxial test with axial loads perpendicular to the laminae and parallel to the laminae. [PERSON] et al. [16] investigated the acoustic emission response characteristics during Brazilian splitting of laminated shale using a digital scattering technique. Based on triaxial compression experiments in two directions and longitudinal and transverse wave velocity tests, the variation patterns of the shale elastic modulus, Poisson's ratio, and longitudinal and transverse wave velocity in different directions were analyzed by [PERSON] et al. [17] to obtain the development characteristics of shale laminae in the Tonghua area of northeast China. [PERSON] et al. [18] discretized the model based on finite differences and obtained the pressure distribution and typical capacity curves in the reservoir matrix and fractures by using Matlab programming. The effects of the permeability and density of laminar fractures on shale oil production capacity were analyzed. [PERSON] et al. [19] carried out three-point bending tests on cylindrical specimens with different orientations of the notch and lamina to study the anisotropic characteristics of shale fracture toughness and reveal the anisotropy of its fracture mechanism and then explored the important role of laminae in the formation of shale reticulation fractures based on the extension law of shale hydraulic fractures under true triaxial conditions. On the other hand, [PERSON] et al. [20] established a full 3D hydraulic fracture flow-solid coupling model considering the influence of laminae based on the 3D displacement discontinuity method and finite difference method. Although scholars at home and abroad have conducted many studies on the mechanism of fracture extension in laminated shale, there is still a lack of systematic research on the theory and influence mechanism of the interaction between hydraulic fractures and laminae in deep shale, so it is crucial to establish a practical numerical simulation research method for the interaction mechanism between laminae and hydraulic fractures.